Lecture2_DataAnalysis_Understanding_Planning_KK.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 학습방향과 알고리즘(Learning Style and Algorithms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 학습방향\n",
    "> **알고리즘은 크게 3 가지 또는 4 가지 문제만을 해결할 수 있음**  \n",
    "> **내가 풀어야 할 문제가 무엇인지 알면 문제 기획/접근/해결 방향은 단순**  \n",
    ">> 1) 문제가 어디에 속하는지 -> \"분석기획(가설/방향)\" 가능  \n",
    ">> 2) 알고리즘마다 입력은 무엇인지 -> \"데이터전처리(준비)\" 가능     \n",
    ">> 3) 알고리즘마다 출력은 무엇인지 -> \"결과해석(설명/검증)\" 가능   \n",
    "\n",
    "- 기계학습의 3가지 분류:  \n",
    "<center><img src='Image/ML_Type_Application_Circle.jpg' width='600'></center>  \n",
    "\n",
    "- 기계학습의 4가지 분류:\n",
    "<center><img src='Image/ML_Type_Application.png' width='600'></center>  \n",
    "\n",
    "- 각 분류별 특성과 역할:  \n",
    "<center><img src='Image/ML_Type_Glance.jpg' width='600'></center>\n",
    "\n",
    "| - | Supervised Learning | Unsupervised Learning | Semi-supervised Learning |\n",
    "|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------|\n",
    "| - | <img src='Image/Supervised-Learning-Algorithms.png' width='150'> | <img src='Image/Unsupervised-Learning-Algorithms.png' width='150'> | <img src='Image/Semi-supervised-Learning-Algorithms.png' width='150'> |\n",
    "| Input Data | labeled | unlabeled | labeled + unlabeled |\n",
    "| Output Result | labeled | unlabeled | labeled + unlabeled |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 학습방향에 따른 알고리즘 [(Summary)](https://en.wikipedia.org/wiki/Outline_of_machine_learning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Supervised Learning\n",
    "\n",
    "| Regression Algorithms | Instance-based Algorithms | Regularization Algorithms | Decision Tree Algorithms | Bayesian Algorithms | Artificial Neural Network Algorithms |\n",
    "|------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------|\n",
    "| <img src='Image/Regression-Algorithms.png' width='150'> | <img src='Image/Instance-based-Algorithms.png' width='150'> | <img src='Image/Regularization-Algorithms.png' width='150'> | <img src='Image/Decision-Tree-Algorithms.png' width='150'> | <img src='Image/Bayesian-Algorithms.png' width='150'> | <img src='Image/Artificial-Neural-Network-Algorithms.png' width='150'> |\n",
    "| Ordinary Least Squares Regression (OLSR) | k-Nearest Neighbor (kNN) | Ridge Regression | Classification and Regression Tree (CART) | Naive Bayes | Perceptron |\n",
    "| Linear Regression | Learning Vector Quantization (LVQ) | Least Absolute Shrinkage and Selection Operator (LASSO) | Iterative Dichotomiser 3 (ID3) | Gaussian Naive Bayes | Back-Propagation |\n",
    "| Logistic Regression | Self-Organizing Map (SOM) | Elastic Net | C4.5 and C5.0 (different versions of a powerful approach) | Multinomial Naive Bayes | Hopfield Network |\n",
    "| Stepwise Regression | Locally Weighted Learning (LWL) | Least-Angle Regression (LARS) | Chi-squared Automatic Interaction Detection (CHAID) | Averaged One-Dependence Estimators (AODE) | Radial Basis Function Network (RBFN) |\n",
    "| Multivariate Adaptive Regression Splines (MARS) | - | - | Decision Stump | Bayesian Belief Network (BBN) | - |\n",
    "| Locally Estimated Scatterplot Smoothing (LOESS) | - | - | M5 | Bayesian Network (BN) | - |\n",
    "| - | - | - | Conditional Decision Trees | - | - |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unsupervised Learning  \n",
    "\n",
    "| Clustering Algorithms | Association Rule Learning Algorithms | Dimensionality Reduction Algorithms | Ensemble Algorithms | Deep Learning Algorithms |\n",
    "|------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------|\n",
    "| <img src='Image/Clustering-Algorithms.png' width='150'> | <img src='Image/Assoication-Rule-Learning-Algorithms.png' width='150'> | <img src='Image/Dimensional-Reduction-Algorithms.png' width='150'> | <img src='Image/Ensemble-Algorithms.png' width='150'> | <img src='Image/Deep-Learning-Algorithms.png' width='150'> |\n",
    "| k-Means | Apriori algorithm | Principal Component Analysis (PCA) | Boosting | Deep Boltzmann Machine (DBM) |\n",
    "| k-Medians | Eclat algorithm | Principal Component Regression (PCR) | Bootstrapped Aggregation (Bagging) | Deep Belief Networks (DBN) |\n",
    "| Expectation Maximisation (EM) | - | Partial Least Squares Regression (PLSR) | AdaBoost | Convolutional Neural Network (CNN) |\n",
    "| Hierarchical Clustering | - | Sammon Mapping | Stacked Generalization (blending) | Stacked Auto-Encoders |\n",
    "| - | - | Multidimensional Scaling (MDS) | Gradient Boosting Machines (GBM) | - |\n",
    "| - | - | Projection Pursuit | Gradient Boosted Regression Trees (GBRT) | - |\n",
    "| - | - | Linear Discriminant Analysis (LDA) | Random Forest | - |\n",
    "| - | - | Mixture Discriminant Analysis (MDA) | - | - |\n",
    "| - | - | Quadratic Discriminant Analysis (QDA) | - | - |\n",
    "| - | - | Flexible Discriminant Analysis (FDA) | - | - |\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time-series Learning\n",
    "\n",
    "- **\"정확성 vs. 설명력 반비례 관계 존재\"**\n",
    "<center><img src='Image/Performance_Explanability.png' width='600'></center>\n",
    "\n",
    "- **분석단계 비교: 선형(회귀분석) vs 비선형(신경망)**\n",
    "\n",
    "| -                            | Linear Model                                            | Neural Network Model                                   |\n",
    "|----------------------------- |-------------------------------------------------------- |------------------------------------------------------- |\n",
    "| **모델특징**                 | -                                                       | -                                                      |\n",
    "| 분석목적                     | 선형성파악(설명가능)                                    | 비선형성파악(설명불가)                                 |\n",
    "| 이론적(수학적) 근거          | 존재                                                    | 미존재                                                 |\n",
    "| **분석단계 특징(전처리)**    | -                                                       | -                                                      |\n",
    "| 데이터 로딩                  | <span style=\"color:blue\">Panel Data</span>              | <span style=\"color:red\">다양(운이좋으면 Panel)</span>  |\n",
    "| 데이터 빈칸 채우기/삭제      | <span style=\"color:red\">분석필요</span>                 | <span style=\"color:red\">분석필요</span>                |\n",
    "| 데이터 컬럼 추가/삭제        | <span style=\"color:red\">분석필요+민감</span>            | <span style=\"color:red\">분석필요+덜민감</span>         |\n",
    "| 데이터 분리                  | <span style=\"color:blue\">Train/Validate/Test</span>     | <span style=\"color:blue\">Train/Validate/Test</span>    |\n",
    "| 데이터 스케일링              | <span style=\"color:red\">분석필요/미필요</span>          | <span style=\"color:red\">분석필요</span>                |\n",
    "| **분석단계 특징(모델링)**    | -                                                       | -                                                      |\n",
    "| 입력 확인 및 변환            | <span style=\"color:blue\">Panel Data</span>              | <span style=\"color:red\">다양(정해지지 않음)</span>     |\n",
    "| 데이터 모델연결              | <span style=\"color:blue\">자동화</span>                  | <span style=\"color:red\">반자동화</span>                |\n",
    "| 비용함수(Cost)               | <span style=\"color:blue\">최소제곱에러(MSE)</span>       | <span style=\"color:red\">다양</span>                    |\n",
    "| 추정함수(Optimizer)          | <span style=\"color:blue\">고정(미분1회 대체가능)</span>  | <span style=\"color:red\">다양(미분지속)</span>          |\n",
    "| **분석단계 특징(검증)**      | -                                                       | -                                                      |\n",
    "| 정확성지표                   | <span style=\"color:red\">다양</span>                     | <span style=\"color:red\">다양</span>                    |\n",
    "| 잔차진단활용                 | <span style=\"color:red\">가능(분석필요)</span>           | <span style=\"color:blue\">불가</span>                   |\n",
    "| **분석단계 특징(결과해석)**  | -                                                       | -                                                      |\n",
    "| 관계성 시각화/영향력 해석    | <span style=\"color:red\">가능(분석필요)</span>           | <span style=\"color:blue\">불가</span>                   |    \n"
   ]
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   "source": [
    "# 시계열 데이터/분석과 기계학습의 차이\n",
    "\n",
    "- **확률 과정(Stochastic Process)**: 상관 관계를 가지는 무한개의 변수의 순서열  \n",
    "\n",
    "<center>$Y$ = {$\\dots$, $Y_{-2}$, $Y_{-1}$, $Y_{0}$, $Y_{1}$, $Y_{2}$, $\\dots$}\n",
    "and\n",
    "$X$ = {$\\dots$, $X_{-2}$, $X_{-1}$, $X_{0}$, $X_{1}$, $X_{2}$, $\\dots$}</center>\n",
    "\n",
    "<center>$X_1$ = {$\\dots$, $X_{1,-2}$, $X_{1,-1}$, $X_{1,0}$, $X_{1,1}$, $X_{1,2}$, $\\dots$}</center>\n",
    "<center>$X_2$ = {$\\dots$, $X_{2,-2}$, $X_{2,-1}$, $X_{2,0}$, $X_{2,1}$, $X_{2,2}$, $\\dots$}</center>\n",
    "\n",
    "- **시계열 데이터(Time Series Data):** 일정한 시간 간격으로 기록된 확률과정의 샘플\n",
    "\n",
    "<center>\n",
    "$y$ = {$\\dots$, $y_{-2}$, $y_{-1}$, $y_{0}$, $y_{1}$, $y_{2}$, $\\dots$} or {$y_t$ : $t$ = $\\dots$, -2, -1, 0, 1, 2, $\\dots$} or $\\{y_t\\}_{-\\infty}^{\\infty}$\n",
    "</center>\n",
    "\n",
    "<center>\n",
    "$x$ = {$\\dots$, $x_{-2}$, $x_{-1}$, $x_{0}$, $x_{1}$, $x_{2}$, $\\dots$} or {$x_t$ : $t$ = $\\dots$, -2, -1, 0, 1, 2, $\\dots$} or $\\{x_t\\}_{-\\infty}^{\\infty}$\n",
    "</center>\n",
    "\n",
    "<center>$x_1$ = {$\\dots$, $x_{1,-2}$, $x_{1,-1}$, $x_{1,0}$, $x_{1,1}$, $x_{1,2}$, $\\dots$} or {$x_{1t}$ : $t$ = $\\dots$, -2, -1, 0, 1, 2, $\\dots$}</center>\n",
    "<center>$x_2$ = {$\\dots$, $x_{2,-2}$, $x_{2,-1}$, $x_{2,0}$, $x_{2,1}$, $x_{2,2}$, $\\dots$} or {$x_{2t}$ : $t$ = $\\dots$, -2, -1, 0, 1, 2, $\\dots$}</center>\n",
    "\n",
    "> - 독립변수($x_t$)와 알고자 하는 종속변수($y_t$)가 시간단위($t$)를 포함  \n",
    "> - 모델의 출력(Output)은 $y$의 시간 $t$에서의 예측값($\\hat{y_t}$)  \n",
    "> - 기계학습과 시계열예측 간 큰 차이가 존재하기에, 시계열 변수생성은 약간의 조정들을 요구함"
   ]
  },
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   "metadata": {},
   "source": [
    "## 대표적인 시계열 변수추출 방향 7종 (Feature Engineering)\n",
    "\n",
    "> **데이터 과학자로서 이미 수동/자동 변수 생성(Feature Engineering)에 익숙하지만, 신규 변수를 생성하는 것은 분석에서 가장 중요하고 시간이 많이 걸리는 작업 중 하나입니다.**\n",
    ">> **\"변수 생성시 주의할 점!\"**  \n",
    ">> 1) 미래의 실제 종속변수 예측값이 어떤 독립/종속변수의 FE에 의해 효과가 있을지 단정할 수 없음  \n",
    ">> 2) 독립변수의 예측값을 FE를 통해 생성될 수 있지만 이는 종속변수의 예측에 오류증가를 야기할 수 있음  \n",
    "\n",
    "\n",
    "- **빈도(Frequency)**: 계절성 패턴(Seasonality)이 나타나기 전까지의 데이터 갯수로 사람이 정해야 함 \n",
    "\n",
    "> 예시: 계설성이 1년에 1회 나타날 경우,  \n",
    "    \n",
    "| Data | frequency |\n",
    "|-----------|-----------|\n",
    "| Annual | 1 |\n",
    "| Quarterly | 4 |\n",
    "| Monthly | 12 |\n",
    "| Weekly | 52 |\n",
    "\n",
    "> 예시: 데이터가 \"일(Day)\" 단위로 수집된 경우,  \n",
    "   \n",
    "| Seasonality | frequency |\n",
    "|-------------|-----------|\n",
    "| Weekly | 7 |\n",
    "| Annual | 365 |\n",
    "\n",
    "> 예시: 데이터가 \"분(Minute)\" 단위로 수집된 경우,  \n",
    "    \n",
    "| Seasonality | frequency |\n",
    "|-------------|-----------|\n",
    "| Hourly | 60 |\n",
    "| Daily | 24 x 60 |\n",
    "| Weekly | 24 x 60 x 7 |\n",
    "| Annual | 24 x 60 x 365 |\n",
    "\n",
    "> 빈도 설정을 위한 Python 함수 옵션: \n",
    "\n",
    "| Alias | Description |\n",
    "|--------|-----------------------|\n",
    "| B | Business day |\n",
    "| D | Calendar day |\n",
    "| W | Weekly |\n",
    "| M | Month end |\n",
    "| Q | Quarter end |\n",
    "| A | Year end |\n",
    "| BA | Business year end |\n",
    "| AS | Year start |\n",
    "| H | Hourly frequency |\n",
    "| T, min | Minutely frequency |\n",
    "| S | Secondly frequency |\n",
    "| L, ms | Millisecond frequency |\n",
    "| U, us | Microsecond frequency |\n",
    "| N, ns | Nanosecond frequency |\n",
    "\n",
    "| Method | Description |\n",
    "|---------|-----------------------------------------------------------|\n",
    "| bfill | Backward fill |\n",
    "| count | Count of values |\n",
    "| ffill | Forward fill |\n",
    "| first | First valid data value |\n",
    "| last | Last valid data value |\n",
    "| max | Maximum data value |\n",
    "| mean | Mean of values in time range |\n",
    "| median | Median of values in time range |\n",
    "| min | Minimum data value |\n",
    "| nunique | Number of unique values |\n",
    "| ohlc | Opening value, highest value, lowest value, closing value |\n",
    "| pad | Same as forward fill |\n",
    "| std | Standard deviation of values |\n",
    "| sum | Sum of values |\n",
    "| var | Variance of values |\n",
    "\n",
    "- **추세(Trend, $T_t$)**: 시계열이 시간에 따라 증가, 감소 또는 일정 수준을 유지하는 경우\n",
    "    - **(수학적 이해)** \n",
    "        - 확률과정의 결정론적 기댓값 함수를 알아내는 것\n",
    "        - 확률과정($Y_t$)이 추정이 가능한 결정론적 추세함수($f(t)$)와 정상확률과정($Y^s_t$)의 합\n",
    "        <center>$Y_t = f(t) + Y^s_t$</center>\n",
    "    \n",
    "\n",
    "<center>\n",
    "<img src='Image/Trend_Increasing.png' width='400'>\n",
    "<img src='Image/Trend_Decreasing.png' width='400'>\n",
    "<img src='Image/Trend_None.png' width='400'>\n",
    "</center>\n",
    "\n",
    "- **계절성(Seasonality, $S_t$)**: 일정한 빈도로 주기적으로 반복되는 패턴($m$), 특정한 달/요일에 따라 기대값이 달라지는 것 \n",
    "> 계설정 반영 방법큰 크게 2가지: 수치값 그대로, 발생 시점으로 분리  \n",
    "> 주기적 패턴이 12개월마다 반복($m$ = 12)  \n",
    "<center><img src='Image/Seasonal.png' width='400'></center>\n",
    "\n",
    "- **주기(Cycle, $C_t$)**: 일정하지 않은 빈도로 발생하는 패턴(계절성) \n",
    "> 빈도가 1인 경우에도 발생 가능($m$ = 1).  \n",
    "<center><img src='Image/Cycle.png' width='400'></center>\n",
    "\n",
    "- **시계열 분해(추세/계절성/잔차(Residual, $e_t$))**:\n",
    "<center><img src='Image/Decomposed-into-its-trend-seasonal-and-irregular.png' width='600'></center>\n",
    "\n",
    "- **더미변수(Dummy Variables, $D_i$)**: 이진수(0 또는 1)의 형태로 변수를 생성하는 것으로 휴일, 이벤트, 캠페인, Outlier 등을 생성 가능\n",
    "    - **생성법:**\n",
    "        1. 범주형 변수(Categorical Variable)의 기준값을 미리 결정 (ex. 계절일 경우 봄)\n",
    "        2. 기준값을 제외한 채 더미변수를 생성 (ex. $D_1$ = 여름, $D_2$ = 가을, $D_3$ = 겨울) \n",
    "        2. 각 더미변수의 값을 0 또는 1로 채우며 1은 각 더미변수의 정의와 같음을 의미\n",
    "        \n",
    "> 확실한 패턴이 존재하는 경우에만 효과가 있으며 오히려 모델의 오류를 증가시킬 수 있음 \n",
    "\n",
    "<center><img src='Image/Dummy-variable-regression.jpg' width='400'></center>\n",
    "\n",
    "- **지연값(Lagged values, $Lag_t(X_1)$)**: 변수의 지연된 값을 독립변수로 반영하는 것으로,ARIMA/VAR/NNAR 등이 활용  \n",
    "<center><img src='Image/Lag-explanation.PNG' width='400'></center>\n",
    "\n",
    "- **시간변수**: 시간변수를 미시/거시 적으로 분리하거나 통합하여 생성된 변수  \n",
    "\n",
    "- **요약**:\n",
    "    >- <U>시계열 구성요소는 각 변수의 시간패턴을 파악하는데 중요\n",
    "    >- <U>FE를 통해 생성된 변수의 입력(Input) 형태로 모형 선택을 하는데 필요 \n",
    "    >- <U>생성된 변수의 패턴이 기존 모델에서 반영하지 않던 패턴이라면 예측 성능을 높임 \n",
    "    >- <U>예측성능 향상 뿐 아니라 결과를 해석하고 해당 속성을 분석하며 가능한 원인 식별에 도움"
   ]
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   },
   "source": [
    "## 데이터준비 방향"
   ]
  },
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   },
   "source": [
    "### 비시계열 데이터준비(General Validation)\n",
    "> **일반적준비(Simple Validation):**\n",
    "- **훈련셋(Training set):** 이름처럼 일반적으로 전체 데이터의 60%를 사용하여 기계학습을 하는데 사용됨  \n",
    "- **검증셋(Validation set):** \n",
    "    - 개발셋이라고도 하며, 일반적으로 전체 데이터의 20%를 사용함\n",
    "    - 훈련된 여러가지 모델들의 성능을 테스트 하는데 사용되며 모델 선택의 기준이 됨\n",
    "- **테스트셋(Testing set):** 전체 데이터의 20%를 사용하며 최종 모델의 정확성을 확인하는 목적에 사용됨\n",
    "\n",
    "<center><img src='Image/DataSplit_Simple.png' width='500'></center>\n",
    "\n",
    "> **$K$교차검사($K$-fold Cross Validation):**  \n",
    "1. 훈련셋을 복원없이 $K$개로 분리한 후, $K-1$는 하위훈련셋으로 나머지 1개는 검증셋으로 사용함  \n",
    "2. 검증셋과 하위훈련셋을 번갈아가면서 $K$번 반복하여 각 모델별로 $K$개의 성능 추정치를 계산  \n",
    "3. $K$개의 성능 추정치 평균을 최종 모델 성능 기준으로 사용  \n",
    "\n",
    "<center><img src='Image/DataSplit_Kfold.png' width='500'></center>\n",
    "\n",
    "> **간단한준비(Holdout Validation):**\n",
    "- **훈련셋(Training set):** 일반적으로 전체 데이터의 70% 사용 \n",
    "- **테스트셋(Testing set):** 일반적으로 전체 데이터의 30% 사용\n",
    "\n",
    "> **$K$-fold vs. Random-subsamples vs. Leave-one-out vs. Leave-$p$-out**  \n",
    ">- **$K$-fold**\n",
    "<center><img src='Image/DataSplit_ver1.png' width='500'></center>\n",
    "\n",
    ">- **Random-subsamples**\n",
    "<center><img src='Image/DataSplit_ver2.png' width='500'></center>\n",
    "\n",
    ">- **Leave-one-out**\n",
    "<center><img src='Image/DataSplit_ver3.png' width='500'></center>\n",
    "\n",
    ">- **Leave-$p$-out**\n",
    "<center><img src='Image/DataSplit_ver4.png' width='500'></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-15T06:45:06.962299Z",
     "start_time": "2019-06-15T06:45:06.947692Z"
    }
   },
   "source": [
    "### 시계열 데이터준비(Time Series Validation)\n",
    ">- **시계열 데이터인 경우 랜덤성(set.seed)을 부여하면 안되고 시간축 유지가 핵심!**\n",
    "    - **훈련셋(Training set):** 가장 오래된 데이터\n",
    "    - **검증셋(Validation set):** 그 다음 최근 데이터\n",
    "    - **테스트셋(Testing set):** 가장 최신의 데이터\n",
    "<center><img src='Image/DataSplit_TimeSeries.png' width='500'></center>\n",
    "\n",
    ">- **과거 정확성이 높더라도 미래의 정확성 보장할 수 없기에, 미래 모든시기 검증 추천!**\n",
    "    - 1스텝 교차검사(One-step Ahead Cross-validation)<center><img src='Image/DataSplit_TimeSeries_ver1.png' width='500'></center>\n",
    "    - 2스텝 교차검사(Two-step Ahead Cross-validation)<center><img src='Image/DataSplit_TimeSeries_ver2.png' width='500'></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 시계열 알고리즘의 2가지 차별화 방향\n",
    ">**\"학습된 도메인 영역 내의 패턴 뿐 아니라 외부 시점의로 데이터를 확장 할 수 있어야 시계열 알고리즘\"**\n",
    "- 시계열 데이터나 FE를 통해 생성된 변수들은 미래시점을 생성시킬 수 있음  \n",
    "- 대다수의 기계학습 알고리즘은 학습된 도메인 영역에서의 패턴만을 추출\n",
    "\n",
    ">**\"시계열 알고리즘은 점추정이 아닌 구간추정 알고리즘으로 설명력 효과에 뿌리를 둠\"**\n",
    "- 대부분의 기계학습 모델은 통계분포에 기반하지 않기 때문에 점추정 알고리즘  \n",
    "- 신뢰구간의 정확성은 확신 할 수 없지만 점추정 보다 다양한 해석을 가능하게 함\n",
    "\n",
    "- **\"정확성 vs. 설명력 반비례 관계 존재\"**\n",
    ">**설명력 최근 연구동향:**\n",
    "    - [LIME](https://blog.fastforwardlabs.com/2017/09/01/LIME-for-couples.html)\n",
    "    - [DARPA](https://bdtechtalks.com/2019/01/10/darpa-xai-explainable-artificial-intelligence/)\n",
    "<center><img src='Image/Performance_Explanability.png' width='600'></center>\n",
    "<center><img src='Image/Performance_Explanability_TimeSeries.png' width='600'></center>\n",
    "\n",
    "\n",
    "- **대표적 알고리즘 예시:**\n",
    "\n",
    "> **Dynamic Linear Model:** \n",
    "  - Bayesian-based Models\n",
    "  - [Generalized Autoregressive Conditional Heteroskedasticity(GARCH)](https://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity)\n",
    "  - [Vector Autoregression(VAR)](https://en.wikipedia.org/wiki/Vector_autoregression)\n",
    "\n",
    "> **Nueral Network Model:**\n",
    "  - Neural Networks Autoregression(NNAR)\n",
    "  - Recurrent Neural Network(RNN)\n",
    "  - Long Short-Term Memory(LSTM)\n",
    "  - Gated Recurrent Unit(GRU)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 검증지표(Evaluation Metrics)과 잔차진단(Residuals Diagnostics) 방향\n",
    ">**\"예측 분석 이후 예측이 잘 되었는지 그리고 데이터의 시간패턴이 잘 추출 되었는지 평가하는 것이 중요합니다.\"**\n",
    "- 검증지표는 예측값과 실제값이 얼마나 비슷한지를 측정하는 것이며, 모형이 시간특성을 잘 잡아내는지를 측정하지는 않음  \n",
    "- 시간특성 패턴이 잘 추출되었는지 확인하기 위해선 잔차(또는 에러) 진단을 통해 백색잡음(White Noise)과 얼마나 유사한지 측정=> <U>\"Residual Diagnostics\" or \"Error Analysis\"</U>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 검증지표(Evaluation Metrics)\n",
    "\n",
    "- **종류**\n",
    "\n",
    "> **1) 문제해결 검증지표:** 문제를 잘 풀었는지 평가하기 위한 기준\n",
    "<center><img src='Image/Evaluation_Metric_Types.png' width='600'></center>\n",
    "\n",
    "> - **Statistical Metrics:** Correlation\n",
    ">> - 입력(Input): -무한대 ~ 무한대 범위의 연속형 값\n",
    ">> - 출력(Output): 이론적으론 -1 ~ 1 범위의 연속형 값\n",
    "> - **Regression Metrics:** MSE, MSPE, RMSE, RMSLE, MAE, MAPE, MPE, R^2, Adjusted R^&2, ... (Y의 범위가 무한대가 가능한 연속형일때)\n",
    ">> - 입력(Input): -무한대 ~ 무한대 범위의 연속형 값\n",
    ">> - 출력(Output): 이론적으론 0 ~ 무한대 범위의 연속형 값\n",
    "> - **Classification Metrics:** Log Loss, Cross-entropy, ROC, AUC, Gini, Confusion Matrix, Accuracy, Precision, Recall, F1-score, Classification Report, KS Statistic, Concordant-Discordant Ratio ... (Y가 2개 또는 그 이상개수의 이산형일때)\n",
    ">> - 입력(Input): -무한대 ~ 무한대 범위의 연속형 값\n",
    ">> - 출력(Output): 알고리즘 종류에 따라 출력이 달라질 수 있음\n",
    ">>> - 확률(Probability): 0 ~ 1 범위의 연속형 값 (Logistic Regression, Random Forest, Gradient Boosting, Adaboost, ...)\n",
    ">>> - 집단(Class): 0 또는 1의 이산형 값 (SVM, KNN, ...)\n",
    "> - **Ranking Metrics:** Gain, Lift, MRR, DCG, NDCG, ...\n",
    "> - **Computer Vision Metrics:** PSNR, SSIM, IoU, ...\n",
    "> - **NLP Metrics:** Perplexity, BLEU score, ...\n",
    "> - **Deep Learning Related Metrics:** Inception score, Frechet Inception distance, ...\n",
    "> - **Real Problem:** ???\n",
    "\n",
    "> **2) 알고리즘비교 검증지표:** 어떤 알고리즘이 더 성능이 좋은지 평가하기 위한 기준   \n",
    "> : 알고리즘 성능이 좋은것과 문제해결이 가능한 것은 다르기에, 알고리즘 검증지표는 없어도 되지만 문제해결 검증지표는 반드시 필요    \n",
    "> : (이론적)알고리즘은 그저 특정 검증지표를 사용하여 만들어짐  \n",
    "> - **Regression:** MSE\n",
    "> - **Logistic Regression:** Log Loss\n",
    "> - **Random Forest:** ???\n",
    "> - **ARIMA:** ???\n",
    "> - **CNN, RNN:** ???\n",
    "> - **Example:** [Comparison of Algorithm Performance Metrics](https://pkg.robjhyndman.com/forecast/reference/accuracy.html)\n",
    "\n",
    "- **예시:** \n",
    "\n",
    "> - **Regression Metrics:** MSE, MSPE, RMSE, RMSLE, MAE, MAPE, MPE, R^2, Adjusted R^&2, ... (Y의 범위가 무한대가 가능한 연속형일때)\n",
    "<center><img src='Image/Evaluation_Metric1.jpg' width='300'></center>  \n",
    "    \n",
    "<center><img src='Image/Evaluation_Metric2.jpg' width='300'></center>  \n",
    "    \n",
    "<center><img src='Image/Evaluation_Metric3.jpg' width='300'></center>  \n",
    "    \n",
    "<center><img src='Image/Evaluation_Metric4.jpg' width='300'></center>  \n",
    "    \n",
    "<center><img src='Image/Evaluation_Metric5.jpg' width='250'></center>\n",
    "\n",
    "> - **Classification Metrics:** Log Loss, Cross-entropy, ROC, AUC, Gini, Confusion Matrix, Accuracy, Precision, Recall, F1-score, Classification Report, KS Statistic, Concordant-Discordant Ratio ... (Y가 2개 또는 그 이상개수의 이산형일때)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 잔차진단(Residual Diagnostics)\n",
    "\n",
    ">**\"백색잡음(White Noise)는 2가지의 속성을 만족해야 하며 하나라도 만족하지 못하면 모델이 개선의 여지가 있음을 의미합니다.\"**  \n",
    "\n",
    "- **백색잡음(White Noise, $WN$):**   \n",
    "<center><img src='Image/White_Noise.png' width='300'></center>\n",
    "    \n",
    ">**1) 잔차들은 정규분포이고, (unbiased) 평균 0과 일정한 분산을 가져야 함:**  \n",
    "\\begin{align*}\n",
    "\\{\\epsilon_t : t = \\dots, -2, -1, 0, 1, 2, \\dots\\} \\sim N(0,\\sigma^2_{\\epsilon_t}) \\\\\n",
    "\\end{align*}\n",
    "\\begin{align*}\n",
    "where~~ \\epsilon_t \\sim  i.i.d(independent~and~identically~distributed) \\\\\n",
    "\\end{align*}\n",
    "\\begin{align*}\n",
    "\\epsilon_t = Y_t - \\hat{Y_t}, \\;\\; E(\\epsilon_t) = 0, \\;\\; Var(\\epsilon_t) = \\sigma^2_{\\epsilon_t} \\\\\n",
    "\\end{align*}\n",
    "\\begin{align*}\n",
    "Cov(\\epsilon_s, \\epsilon_k) = 0~for~different~times!(s \\ne k)\n",
    "\\end{align*}\n",
    "    \n",
    ">**2) 잔차들이 시간의 흐름에 따라 상관성이 없어야 함:**  \n",
    "- 자기상관함수(Autocorrelation Fundtion([ACF](https://en.wikipedia.org/wiki/Autocorrelation)))를 통해 $Autocorrelation~=~0$인지 확인\n",
    "    - 공분산(Covariance): \n",
    "    <center>$Cov(\\epsilon_s, \\epsilon_k)$ = $E[(\\epsilon_s-E(\\epsilon_s))$$(\\epsilon_k-E(\\epsilon_k))]$ = $\\gamma_{s,k}$</center>\n",
    "    - 자기상관함수(Autocorrelation Function): \n",
    "    <center>$Corr(\\epsilon_s, \\epsilon_k)$ = $\\dfrac{Cov(\\epsilon_s, \\epsilon_k)}{\\sqrt{Var(\\epsilon_s)Var(\\epsilon_k)}}$ = $\\dfrac{\\gamma_{s,k}}{\\sqrt{\\gamma_s \\gamma_k}}$</center>\n",
    "    - 편자기상관함수(Partial Autocorrelation Function): $s$와 $k$사이의 상관성을 제거한 자기상관함수\n",
    "    <center>$Corr[(\\epsilon_s-\\hat{\\epsilon}_s, \\epsilon_{s-t}-\\hat{\\epsilon}_{s-t})]$ for $1<t<k$</center>\n",
    "            \n",
    "            \n",
    "- **회귀분석 가정과의 비교:**\n",
    "    - 종속변수와 독립변수 간에 선형성의 관계를 가져야 함\n",
    "    - 독립변수들 간에 서로 독립이어야 함\n",
    "    - 잔차의 분포가 정규분포이어야 함\n",
    "    - 잔차들이 서로 독립적으로 움직여야 함\n",
    "    - 잔차들의 분산이 서로 같아야 함\n",
    "\n",
    "\n",
    "- **자기상관 테스트 활용예시:**\n",
    "    - Apply a portmanteau test to check the hypothesis that residuals are uncorrelated.\n",
    "    <center><img src='Image/Portmanteau_Test.jpg' width='600'></center>\n",
    "    - Plot the Autocorrelation function (ACF) and evaluate that at least 95% of the spikes are on the interval.\n",
    "    <center><img src='Image/Residual_Plot.png' width='700'></center>    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 시계열이 분석효과에 도움 될 시간영역(해상도)을 선택해야 함\n",
    "> **예측 정확성이 높은 시간영역을 선택하는 것이 좋습니다.**\n",
    "<center><img src='Image/Reduce_Error.png' width='400'></center>\n",
    "\n",
    "- **활용예시:**\n",
    "    - **분석목적:** 연간단위 비즈니스 목표를 예측\n",
    "        - Aim for the most granular level possible.  \n",
    "        - 일반적으로 월별 또는 분기별 데이터를 사용하면 연간 데이터보다 나은 예측이 가능할 것\n",
    "        - 월/분기별 예측치를 연간으로 환산시 오류가 늘어날 것 같지만 실제로는 반대의 경우가 많음  \n",
    "        - 만약 너무 세분화된 시간영역을 사용할 시 오류가 증가될 수 있음\n",
    "            - 연간 비즈니스 목표를 예측하는데 일별/시간별/분별/이하단위의 데이터를 사용하면 도움이 될까?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 시계열 데이터/분석은 높은 정확도를 낳거나 높은 에러를 발생시킴\n",
    "- **높은정확도(High Accuracy):** 과거 패턴이 미래에도 그대로 유지가 된다면 예측 정확도가 높아짐  \n",
    "- **높은에러(High Error):** 패턴이 점차적으로 또는 갑자기 변경되면 예측값은 실제값에서 크게 벗어날 수 있음  \n",
    "    - **Black Swan:** <U>일어날 것 같지 않은 일이 일어나는 현상</U>\n",
    "    - **White Swan:** <U>과거 경험들로 충분히 예상되는 위기지만 대응책이 없고 반복될 현상</U>\n",
    "    - **Gray Swan:** <U>과거 경험들로 충분히 예상되지만 발생되면 충격이 지속되는 현상</U>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 시계열 데이터 관리는 장/단점 존재\n",
    "- 수천/수백만/수십억 데이터를 기계학습에 사용할 수 있지만 시계열로 데이터를 정리하면 데이터 감소 발생가능\n",
    "- 모든 시간범위가 예측성능에 도움되지 않을 수 있기에 특정기간의 시간영역 분석만 필요할 수도 있음\n",
    "\n",
    "- **고성능 시계열 Database 필요:**\n",
    "> [Time Series Database(TSDB)](http://shop.oreilly.com/product/0636920035435.do)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# (시계열) 회귀분석 요약\n",
    "\n",
    "> **\"$t$개의 값을 가지는 $k$차원 독립변수 $X_i$와 이에 대응하는 종속변수 $Y$간의 관계를 정량적으로 찾는 알고리즘\"**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 모델링  \n",
    "\n",
    "- **알고리즘:** 독립 변수나 종속 변수가 반드시 대칭 분포를 보여야 한다는 가정은 없지만 정규 분포에 가까운 분포를 보일 수록 선형회귀모형의 성능이 좋아지는 경우가 많음  \n",
    "\n",
    "<center>\n",
    "$Y \\approx \\hat{Y} = f(X_1, X_2, ..., X_k) = \\beta_0 + \\beta_1X_1 + \\beta_2X_2 + \\cdots + \\beta_kX_k \\\\\n",
    "= [\\beta_0~\\beta_1~\\beta_2~\\cdots~\\beta_k]\\begin{bmatrix} 1 \\\\ X_1 \\\\ X_2 \\\\ \\vdots \\\\ X_k \\end{bmatrix}\n",
    "= [1~X_1~X_2~\\cdots~X_k]\\begin{bmatrix} \\beta_0 \\\\ \\beta_1 \\\\ \\beta_2 \\\\ \\vdots \\\\ \\beta_k \\end{bmatrix}\n",
    "= \\begin{bmatrix} 1~X_{11}~X_{21}~\\cdots~X_{k1} \\\\ 1~X_{12}~X_{22}~\\cdots~X_{k2} \\\\ \\vdots \\\\ 1~X_{1t}~X_{2t}~\\cdots~X_{kt} \\end{bmatrix}\n",
    "\\begin{bmatrix} \\beta_0 \\\\ \\beta_1 \\\\ \\beta_2 \\\\ \\vdots \\\\ \\beta_k \\end{bmatrix} = X\\beta$\n",
    "</center>\n",
    "\n",
    "- **비선형변수 효과:** 로그 또는 제곱근 등의 변환된 변수 사용시 회귀분석 성능 향상 가능\n",
    "    - 독립 변수나 종속 변수가 심하게 한쪽으로 치우친 분포를 보이는 경우\n",
    "    - 독립 변수와 종속 변수간의 관계가 곱셈 혹은 나눗셉으로 연결된 경우\n",
    "    - 종속 변수와 예측치가 비선형 관계를 보이는 경우"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 검증방항(계수추정) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 결정론적 모형(Deterministic Model)\n",
    "> **\"잔차제곱합(Residual Sum of Squares)을 최소로하는 $\\beta$를 추정\"**  \n",
    "\n",
    "**1) 잔차벡터(Residual Vector):** \n",
    "<center>$\\epsilon = Y - \\hat{Y} = Y - X\\beta$</center> \n",
    "\n",
    "**2) 잔차제곱합(Residual Sum of Squares):** \n",
    "<center>$RSS = \\epsilon^T\\epsilon = (Y - X\\beta)^T(Y - X\\beta) = Y^TY-2Y^TX\\beta+\\beta^TX^TX\\beta$</center> \n",
    "\n",
    "**3) 잔차제곱합의 그레디언트(Gradient):** \n",
    "<center>$\\dfrac{dRSS}{d\\beta} = -2X^TY + 2X^TX\\beta$</center> \n",
    "\n",
    "**4) 잔차가 최소가 되는 최적화 조건은 최저점에서의 그레디언트(미분,기울기)이 0이 되어야 함:** \n",
    "<center>$\\dfrac{dRSS}{d\\beta} = 0$</center> \n",
    "\n",
    "**5) 최적화를 위한 잔차제곱합의 그레디언트(Gradient):** \n",
    "<center>$\\dfrac{dRSS}{d\\beta} = -2X^TY + 2X^TX\\beta = 0 \\\\ X^TX\\beta = X^TY$</center> \n",
    "\n",
    "**6) 추정된 계수:** \n",
    "<center>$\\beta = (X^TX)^{-1}X^TY$</center>    \n",
    "\n",
    "- **Summary:**\n",
    "    - $X^TX$ 행렬이 역행렬이 존재해야 해 추정/존재 가능  \n",
    "    - 역행렬이 미존재  \n",
    "    = $X$가 서로 독립이 아님  \n",
    "    = $X$가 Full Rank가 아님  \n",
    "    = $X^TX$가 양의 정부호(Positive Definite)가 아님\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 확률론적 모형(Probabilistic Model)\n",
    "> **\"종속변수의 발생가능성을 최대(최소)로하는 $\\beta$를 추정\"**\n",
    "- **필요성:** 결정론적 선형 회귀모형(OLS)는 데이터의 확률론적 가정이 없기에 단하나의 가중치(점추정)를 계산하나, 이 가중치의 신뢰도(구간추정)는 확인할 수 없음\n",
    "- **예시:** 집값에 대한 범죄율 영향력(가중치)이 -0.108이라면, 집값은 범죄율에 반비례한다 결론 내릴 수 있을까?\n",
    "    - -0.108는 오로지 우리가 보유한 테스트 1회성 결과일 뿐 오차가 존재가능\n",
    "    - 만약 오차가 0.0001이라면 실제 가중치 신뢰구간은 -0.108$\\pm$0.0001 (-0.1081 ~ -0.1079)이기에 집값과 범죄율 반비례 결론 가능\n",
    "    - 만약 오차가 0.2라면 실제 가중치는 (-0.308 ~ 0.092)이기에 가중치는 0이나 양수도 가능 -> 집값과 범죄율은 정비례도 가능\n",
    "\n",
    "\\begin{align*}\n",
    "\\text{Main Equation} && Y \\approx \\hat{Y} &= f(X_1, X_2, ..., X_k) \\\\\n",
    "&& &= \\beta_0 + \\beta_1X_1 + \\beta_2X_2 + \\cdots + \\beta_kX_k \\\\\n",
    "&& &= E(Y|X_1, X_2, ... , X_k) \\\\ \n",
    "&& &\\sim \\mathcal{N}(X \\beta, \\sigma^2) \\\\\n",
    "&& p(Y \\mid X, \\theta) &= \\mathcal{N}(y \\mid X \\beta, \\sigma^2 ) \\\\\n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "\\text{Error Poperties} && p(\\epsilon \\mid \\theta) &= \\mathcal{N}(0, \\sigma^2 ) \\text{  from  } \\epsilon = Y - X \\beta \\\\\n",
    "&& \\text{E}(\\epsilon \\mid X) &= 0 \\\\\n",
    "&& \\text{E}(\\epsilon) &= \\text{E}(\\text{E}(\\epsilon \\mid X)) = 0 \\\\\n",
    "&& \\text{E}(\\epsilon X) &= \\text{E}(\\text{E}(\\epsilon X \\mid X)) = \\text{E}(X \\text{E}(\\epsilon\\mid X)) = 0 \\\\\n",
    "&& \\text{E}(\\epsilon^2) &= \\sigma^2 (N-K) \\\\\n",
    "&& \\text{Cov}(\\epsilon_i, \\epsilon_j \\mid X) &= 0 \\;\\; (i,j=1,2,\\ldots,N)\n",
    "\\end{align*}\n",
    "\n",
    "- **Summary:**\n",
    "    - $X, Y$ 중 어느 것도 정규분포일 필요는 없음  \n",
    "    - $Y$는 $X$에 대해 조건부로 정규분포를 따르며 $Y$자체가 무조건부로 정규분포일 필요는 없음  \n",
    "    - 잔차의 기대값은 0  \n",
    "    - 잔차의 조건부 기대값은 0  \n",
    "    - 잔차와 독립변수 $X$는 상관관계 없음  \n",
    "    - $X$와 무관하게 잔차들간의 공분산은 0  \n",
    "    \n",
    "**1) Y의 발생가능성(Likelihood):** \n",
    "\n",
    "\\begin{align*}\n",
    "p(Y_{1:N} \\,\\big|\\, X_{1:N}, \\theta) &= \\prod_{i=1}^N \\mathcal{N}(Y_i \\,\\big|\\, X_i \\beta_i , \\sigma^2) \\\\\n",
    "&= \\prod_{i=1}^N \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left\\{-\\frac{(Y_i- X_i \\beta_i)^2}{2\\sigma^2} \\right\\}\n",
    "\\end{align*}\n",
    "\n",
    "**2) 더하기 사용을 위한 Log 변환(Log-Likelihood):** \n",
    "\n",
    "\\begin{align*}\n",
    "\\text{LL} &= \\log p(Y_{1:N} \\,\\big|\\, X_{1:N}, \\theta) \\\\\n",
    "&= \\log \\prod_{i=1}^N \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left\\{-\\frac{(Y_i-X_i \\beta_i)^2}{2\\sigma^2} \\right\\}  \\\\\n",
    "&= -\\dfrac{1}{2\\sigma^2} \\sum_{i=1}^N (Y_i-X_i \\beta_i)^2 - \\dfrac{N}{2} \\log{2\\pi}{\\sigma^2}  \\\\\n",
    "\\text{LL(Matrix Form)} &= -C_1 (Y - X\\beta)^T(y-X\\beta) - C_0 \\\\\n",
    "&= -C_1(\\beta^TX^TX\\beta -2 Y^TX\\beta + Y^TY) - C_0 \\\\\n",
    "& \\text{where } C_1=  -\\dfrac{1}{2\\sigma^2}, C_0 =  \\dfrac{N}{2} \\log{2\\pi}{\\sigma^2} \\\\\n",
    "\\end{align*}\n",
    "\n",
    "**3) Log-Likelihood의 그레디언트(미분,기울기)는 0이 되어야 함:** \n",
    "\n",
    "\\begin{align*}\n",
    "\\dfrac{d}{d\\beta} \\text{LL} &= -C_1 \\left( 2X^TX \\hat{\\beta} - 2X^TY \\right) = 0 \\\\\n",
    "\\hat{\\beta} &= (X^TX)^{-1}X^T Y \\\\\n",
    "\\end{align*}\n",
    "\n",
    "- **Summary:**\n",
    "    - $X^TX$ 행렬이 역행렬이 존재해야 해 추정/존재 가능  \n",
    "    - 역행렬이 미존재  \n",
    "    = $X$가 서로 독립이 아님  \n",
    "    = $X$가 Full Rank가 아님  \n",
    "    = $X^TX$가 양의 정부호(Positive Definite)가 아님\n",
    "    \n",
    "\n",
    "- **회귀계수의 분포:**\n",
    "\n",
    "\\begin{align*}\n",
    "\\text{Main Equation} && \\hat{\\beta} &= (X^TX)^{-1} X^T Y \\\\\n",
    "&& &= (X^TX)^{-1} X^T (X \\beta + \\epsilon) \\\\\n",
    "&& &= \\beta + (X^TX)^{-1} X^T \\epsilon \\\\\n",
    "\\text{Expectation} && \\text{E}(\\hat{\\beta}) &=  \\text{E}( \\beta + (X^TX)^{-1} X^T \\epsilon ) \\\\\n",
    "&& &=  \\beta + (X^TX)^{-1} X^T \\text{E}( \\epsilon ) \\\\\n",
    "&& &= \\beta \\\\\n",
    "\\text{Variance} && \\text{Var}(\\hat{\\beta}_i)  &= \\left( \\text{Cov}(\\hat{\\beta}) \\right)_{ii} \\;\\; (i=0, \\ldots, K-1) \\\\\n",
    "\\text{Covariance} && \\text{Cov}(\\hat{\\beta}) &= E\\left((\\hat{\\beta} - \\beta)(\\hat{\\beta} - \\beta)^T \\right) \\\\\n",
    "&& &= E\\left(((X^TX)^{-1} X^T \\epsilon)((X^TX)^{-1} X^T \\epsilon)^T \\right) \\\\\n",
    "&& &= E\\left((X^TX)^{-1} X^T \\epsilon \\epsilon^T X(X^TX)^{−1} \\right) \\\\\n",
    "&& &= (X^TX)^{-1} X^T E(\\epsilon \\epsilon^T) X(X^TX)^{−1} \\\\\n",
    "&& &= (X^TX)^{-1} X^T (\\sigma^2 I) X(X^TX)^{−1} \\\\\n",
    "&& &= \\sigma^2  (X^TX)^{-1} \\\\\n",
    "\\text{Standard Deviation} && \\sqrt{\\text{Var}(\\hat{\\beta}_i)} \\approx {se_{\\hat{\\beta}_i}} &= \\sqrt{\\sigma^2 \\big((X^TX)^{-1}\\big)_{ii}} \\;\\; (i=0, \\ldots, K-1) \\\\\n",
    "\\text{Asymptotic} && \\dfrac{\\hat{\\beta}_i - \\beta_i}{se_{\\hat{\\beta}_i}} &\\sim t_{N-K} \\;\\; (i=0, \\ldots, K-1) \\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 검증(Evaluation)\n",
    "\n",
    "- **검증지표(Metrics):** \n",
    "\n",
    "**1) R-squared(R^2):** 추정된 (선형)모형이 주어진 데이터에 잘 적합된 정도, $(- \\infty, 1]$  \n",
    "<center>\n",
    "$R^2$ = $\\dfrac{ESS}{TSS}$ = $\\dfrac{\\sum_{i=1}^{n} (\\hat{y}_i - \\bar{y})^2}{\\sum_{i=1}^{n} (y_i - \\bar{y})^2}$ = $1 - \\dfrac{RSS}{TSS}$ = $1 - \\dfrac{\\sum_{i=1}^{n} (y_i - \\hat{y}_i)^2}{\\sum_{i=1}^{n} (y_i - \\bar{y})^2}$\n",
    "</center>\n",
    "\n",
    "> <center><img src='Image/R2_decomposition1.png' width='600'></center>\n",
    "\n",
    "> <center><img src='Image/R2_decomposition2.png' width='600'></center>\n",
    "\n",
    "- **(비수학적 이해)**\n",
    "    - TSS: 종속변수값의 움직임의 범위\n",
    "    - ESS: 모형에서 나온 예측값의 움직임의 범위\n",
    "    - RSS: 잔차의 움직임의 범위, 즉 오차의 크기\n",
    "    > 모형 예측치의 움직임의 크기(분산)은 종속변수의 움직임의 크기(분산)보다 클 수 없다  \n",
    "    > 모형의 성능이 좋을수록 모형 예측치의 움직임의 크기는 종속변수의 움직임의 크기와 비슷해진다  \n",
    "\n",
    "**2) t-검정:** t분포를 따르는 추정계수로 독립변수와 종속변수 간의 선형관계(관련성) 존재 의사결정을 위한 신뢰성 정도\n",
    "\n",
    "- **검정통계량(t-통계량)**: <center>$t = \\dfrac{\\hat{\\beta}_i - \\beta_i}{se_{\\hat{\\beta}_i}}$</center>  \n",
    "    \n",
    "    - $t$ 값이 작다는 것은 표준편차가 크다는 것 -> 독립변수와 종속변수의 상관성이 낮음  \n",
    "    - $t$ 값이 크다는 것은 표준편차가 작다는 것 -> 독립변수와 종속변수의 상관성이 높음  \n",
    "\n",
    ">- **가설확인**\n",
    "    - **대중주장(귀무가설, Null Hypothesis, $H_0$)**  \n",
    "    : $\\beta_i = 0 \\;\\; (i=0, \\ldots, K-1)$ / 추정계수는 0이다 / 독립변수와 종속변수의 상관관계(선형관계)가 없다\n",
    "    - **나의주장(대립가설, Alternate Hypothesis, $H_1$)**  \n",
    "    : $\\beta_i \\neq 0 \\;\\; (i=0, \\ldots, K-1)$ / 추정계수는 0이 아니다 / 독립변수와 종속변수의 상관관계(선형관계)가 있다\n",
    "> - **의사결정**\n",
    "    - **p-value >= 내기준(ex. 0.05):** 내가 분석한 계수는 대중주장과 유사하기 때문에 대중주장 참 & 나의주장 거짓  \n",
    "    : **분석한 변수는 모델링에 영향력이 없다**\n",
    "    - **p-value < 내기준(ex. 0.05):** 내가 분석한 계수는 대중주장을 벗어나기 때문에 대중주장 거짓 & 나의주장 참  \n",
    "    : **분석한 변수는 모델링에 영향력이 있다**\n",
    "\n",
    "\n",
    "**3) 분산분석을 통한 F-검정:**\n",
    "- **필요성:** \n",
    "    - 변수의 단위 즉, 스케일이 달라지면 회귀분석과 상관없이 잔차제곱합(Residula Sum of Square) 달라짐  \n",
    "    - 분산 분석(Analysis of Variance(ANOVA))은 종속변수의 분산과 독립변수의 분산간의 관계를 사용하여 성능 평가  \n",
    "\n",
    "\n",
    "- **검정통계량(F-통계량):** 분산분석표(ANOVA Table)를 통해 쉽게 계산되며, $T$는 데이터의 갯수, $K$는 변수의 갯수\n",
    "\n",
    "| Source | Degree of Freedom | Sum of Square | Mean Square | F test-statstics | p-value |\n",
    "|------------|-------------------|---------------|------------------------------------------|-------------------------------------------------------|-----------|\n",
    "| Regression | $K-1$ | $ESS$ | $\\sigma_{\\hat{Y}}^2 = \\dfrac{ESS}{K-1}$ | $F = \\dfrac{\\sigma_{\\hat{Y}}^2}{\\sigma_{\\epsilon}^2}$ | $p-value$ |\n",
    "| Residual | $T-K$ | $RSS$ | $\\sigma_{\\epsilon}^2 = \\dfrac{RSS}{T-K}$ | - | - |\n",
    "| Total | $T-1$ | $TSS$ | $\\sigma_{Y}^2 = \\dfrac{TSS}{T-1}$ | - | - |\n",
    "| $R^2$ | - | $ESS/TSS$ | - | - | - |\n",
    "\n",
    "<center>$\\dfrac{ESS}{K-1} \\div \\dfrac{RSS}{T-K} \\sim F(K-1, T-K)$</center>\n",
    "\n",
    ">- **가설확인**\n",
    "    - **대중주장(귀무가설, Null Hypothesis, $H_0$)**  \n",
    "    : $\\beta_0  = \\beta_1 = \\cdots = \\beta_{K-1} = 0$ / 모든 추정계수는 0이다 / 모형은 아무 효과가 없다 / $R^2$ = 0\n",
    "    - **나의주장(대립가설, Alternate Hypothesis, $H_1$)**  \n",
    "    : $\\beta_0  \\neq \\beta_1 \\neq \\cdots \\neq \\beta_{K-1} \\neq 0$ / 모든 추정계수는 0이 아니다 / 모형은 효과가 있다 / $R^2 \\neq 0$  \n",
    "\n",
    "> - **의사결정**\n",
    "    - **p-value >= 내기준(ex. 0.05):** 내가 분석한 결과는 대중주장과 유사하기 때문에 대중주장 참 & 나의주장 거짓  \n",
    "    : **분석한 모델링은 효과가 없다 / 모델은 데이터 패턴을 잘 추정하지 못한다**\n",
    "    - **p-value < 내기준(ex. 0.05):** 내가 분석한 결과는 대중주장을 벗어나기 때문에 대중주장 거짓 & 나의주장 참  \n",
    "    : **분석한 모델링은 효과가 있다 / 모델은 데이터 패턴을 잘 추정한다**\n",
    "    \n",
    "**3) 정보량기준(Information Criterion):** 회귀분석 외에도 다양한 알고리즘에 활용, 값이 작을수록 올바른 모형 (Likelihood는 클수록 올바른 모형)\n",
    "\n",
    "- **[AIC(Akaike Information Criterion)](https://en.wikipedia.org/wiki/Akaike_information_criterion)**  \n",
    ": 모형과 데이터의 확률 분포 사이의 Kullback-Leibler 수준을 가장 크게하기 위한 시도 \n",
    "\n",
    "<center>$AIC = -2log(L) + 2K$</center>\n",
    "<center>($L$: likelihood, $K$: 추정할 파라미터의 수(일반적으로 column수))</center>\n",
    "\n",
    "- **[BIC(Bayesian Information Criterion)](https://en.wikipedia.org/wiki/Bayesian_information_criterion)**  \n",
    ": 데이터가 exponential family라는 가정하에 주어진 데이터에서 모형의 likelihood를 측정하기 위한 값에서 유도 \n",
    "\n",
    "<center>$BIC = -2log(L) + Klog(T)$</center>\n",
    "<center>($L$: likelihood, $K$: 추정할 파라미터의 수(일반적으로 column수), $T$: 데이터의 수(일반적으로 row수))</center>\n",
    "\n",
    "<center><img src='Image/AIC_BIC.gif' width='600'></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 잔차진단(Residual Diagnostics)\n",
    "\n",
    "- **회귀분석 가정 내:**\n",
    "    - ~~종속변수와 독립변수 간에 선형성의 관계를 가져야 함~~\n",
    "    - ~~독립변수들 간에 서로 독립이어야 함~~\n",
    "    - 잔차의 분포가 정규분포이어야 함\n",
    "    - 잔차들이 서로 독립적으로 움직여야 함\n",
    "    - 잔차들의 분산이 서로 같아야 함\n",
    "    \n",
    "    \n",
    "- **시계열 회귀분석 잔차진단 차이 적용:**\n",
    "    - 정상성 테스트: 잔차가 백색잡음의 형태인지\n",
    "    - 정규분포 테스트: 잔차가 정규분포의 형태인지\n",
    "    - 자기상관 테스트: 잔차가 서로 시간흐름에서 독립적인지\n",
    "    - 등분산성 테스트: 잔차가 분산이 일정한지"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 시계열 분석"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 분석 주 사용 패키지"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  \"statsmodels\"\n",
    "\n",
    "> **R-style 모형 기술을 가능하게 하는 patsy 패키지를 포함하고 있어 R에서만 가능했던 회귀 분석 / 시계열 분석을 그대로 파이썬에서 이용가능**\n",
    "- 검정 및 추정(test and estimation)\n",
    "- 회귀 분석(regression analysis)\n",
    "- 시계열 분석(time-series analysis)\n",
    "\n",
    "~~~\n",
    "get_rdataset(item, [package=\"datasets\"])\n",
    "~~~\n",
    "\n",
    "- **statsmodels 데이터셋 예시:**  \n",
    "\n",
    "~~~\n",
    "#대기중 CO2농도 데이터\n",
    "data = sm.datasets.get_rdataset(\"CO2\", package=\"datasets\")\n",
    "#황체형성 호르몬(Luteinizing Hormone)의 수치를 나타내는 시계열 데이터\n",
    "data = sm.datasets.get_rdataset(\"lh\")\n",
    "#1974-1979년 사이의 영국의 호흡기 질환 사망자 수를 나타내는 시계열 데이터\n",
    "data = sm.datasets.get_rdataset(\"deaths\", \"MASS\")\n",
    "#1949-1960년 사이의 국제 항공 운송인원을 나타내는 시계열 데이터\n",
    "data = sm.datasets.get_rdataset(\"AirPassengers\")\n",
    "#미국의 강수량 데이터\n",
    "data = sm.datasets.get_rdataset(\"precip\")\n",
    "#타이타닉호의 탑승자들에 대한 데이터\n",
    "data = sm.datasets.get_rdataset(\"Titanic\", package=\"datasets\")\n",
    "~~~  \n",
    "\n",
    "\n",
    "- **Output:**\n",
    "    - package: 데이터를 제공하는 R 패키지 이름\n",
    "    - title: 데이터 이름\n",
    "    - data: 데이터를 담고 있는 데이터프레임\n",
    "    - __doc__: 데이터에 대한 설명 문자열(R 패키지의 내용 기준)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### \"sklearn\"(scikit-learn)\n",
    "\n",
    "> - 벤치마크용 데이터셋 예제\n",
    "- 데이터 전처리(preprocessing)\n",
    "- 지도 학습(Supervised learning)\n",
    "- 비지도 학습(Unsupervised learning)\n",
    "- 모형 평가 및 선택(evaluation and selection)\n",
    "\n",
    "\n",
    "- **sklearn 데이터셋 예시:**\n",
    "\n",
    "    1) scikit-learn 설치 패키지에 같이 포함된 소량의 데이터(load 계열 명령)\n",
    "    \n",
    "~~~\n",
    "- load_boston: 회귀 분석용 보스턴 집값\n",
    "- load_diabetes: 회귀 분석용 당뇨병 자료\n",
    "- load_linnerud: 회귀 분석용 linnerud 자료\n",
    "- load_iris: 분류용 붓꽃(iris) 자료\n",
    "- load_digits: 분류용 숫자(digit) 필기 이미지 자료\n",
    "- load_wine: 분류용 포도주(wine) 등급 자료\n",
    "- load_breast_cancer: 분류용 유방암(breast cancer) 진단 자료\n",
    "~~~\n",
    "\n",
    "    2) 인터넷에서 다운로드할 수 있는 대량의 데이터(fetch 계열 명령)\n",
    "\n",
    "~~~\n",
    "- fetch_california_housing: : 회귀분석용 캘리포니아 집값 자료\n",
    "- fetch_covtype : 회귀분석용 토지 조사 자료\n",
    "- fetch_20newsgroups : 뉴스 그룹 텍스트 자료\n",
    "- fetch_olivetti_faces : 얼굴 이미지 자료\n",
    "- fetch_lfw_people : 유명인 얼굴 이미지 자료\n",
    "- fetch_lfw_pairs : 유명인 얼굴 이미지 자료\n",
    "- fetch_rcv1 : 로이터 뉴스 말뭉치\n",
    "- fetch_kddcup99 : Kddcup 99 Tcp dump 자료\n",
    "~~~\n",
    "\n",
    "    3) 확률분포를 사용하여 가상의 데이터를 생성(make 계열 명령)\n",
    "\n",
    "~~~\n",
    "- make_regression: 회귀 분석용 가상 데이터 생성\n",
    "- make_classification: 분류용 가상 데이터 생성\n",
    "- make_blobs: 클러스터링용 가상 데이터 생성\n",
    "~~~\n",
    "\n",
    "- **Output:** Bunch 라는 클래스 객체 형식으로 생성, 이 클래스 객체는 다음과 같은 속성을 가짐.\n",
    "    - data: (필수) 독립 변수 ndarray 배열\n",
    "    - target: (필수) 종속 변수 ndarray 배열\n",
    "    - feature_names: (옵션) 독립 변수 이름 리스트\n",
    "    - target_names: (옵션) 종속 변수 이름 리스트\n",
    "    - DESCR: (옵션) 자료에 대한 설명\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 데이터준비 방향"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 시계열 데이터준비(Time Series Validation)\n",
    ">- 시계열 데이터인 경우 랜덤성(set.seed)을 부여하면 안되고 시간축 유지가 핵심!\n",
    "    - **훈련셋(Training set):** 가장 오래된 데이터\n",
    "    - **검증셋(Validation set):** 그 다음 최근 데이터\n",
    "    - **테스트셋(Testing set):** 가장 최신의 데이터\n",
    "<center><img src='Image/DataSplit_TimeSeries.png' width='500'></center>\n",
    "\n",
    ">- **1스텝 교차검사(One-step Ahead Cross-validation)**\n",
    "<center><img src='Image/DataSplit_TimeSeries_ver1.png' width='500'></center>\n",
    "\n",
    ">- **2스텝 교차검사(Two-step Ahead Cross-validation)**\n",
    "<center><img src='Image/DataSplit_TimeSeries_ver2.png' width='500'></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 전처리 방향"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 시간현실 반영\n",
    "> **\"미래의 시간패턴을 미리 반영하는건 비현실적, 이는 과적합(Overfitting)을 유발\"**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 예측 정확성 향상\n",
    "\n",
    "> **방향:  \n",
    "1) Train $\\uparrow$ + Test $\\uparrow$  \n",
    "2) Train <<< Test $\\Longleftrightarrow$ 조건수(Condition Number) 감소**  \n",
    "\n",
    "- **조건수 감소 목적:**\n",
    "    - **(비수학적 이해)**  \n",
    "    : 독립변수들의 절대적 수치크기나 서로간의 의존도가 분석결과에 주는 영향을 줄이고 독립변수의 상대적인 비교효과 반영\n",
    "    - **(수학적 이해)**  \n",
    "    : 공분산 행렬의 변동성을 줄여 분석결과의 변동을 줄임\n",
    "        > **공분산 행렬의 변동성?:** 모델링 계수추정시 영향을 주는 역행렬에 오차가 미치는 영향\n",
    "           \n",
    "<center>\n",
    "$조건수(Condition~Number) = \\dfrac{\\lambda_{max}}{\\lambda_{min}} \\\\ where \\\\\n",
    "\\lambda_{max} = max[eigenvalue\\{Cov(X^T X)\\}] \\\\\n",
    "\\lambda_{min} = min[eigenvalue\\{Cov(X^T X)\\}]$\n",
    "</center>  \n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-06T14:14:44.053232Z",
     "start_time": "2020-09-06T14:14:44.049240Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0.],\n",
       "       [0., 1., 0., 0.],\n",
       "       [0., 0., 1., 0.],\n",
       "       [0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 조건수가 작을 때\n",
    "# X 데이터\n",
    "import numpy as np\n",
    "A = np.eye(4)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-06T14:06:38.333041Z",
     "start_time": "2020-09-06T14:06:38.322069Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1.])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Y 데이터\n",
    "Y = np.ones(4)\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-06T14:09:15.272349Z",
     "start_time": "2020-09-06T14:09:15.249409Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1.])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 계수 추정\n",
    "np.linalg.solve(A, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-06T14:09:39.087158Z",
     "start_time": "2020-09-06T14:09:39.080177Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.0001, 0.    , 0.    , 0.    ],\n",
       "       [0.    , 1.0001, 0.    , 0.    ],\n",
       "       [0.    , 0.    , 1.0001, 0.    ],\n",
       "       [0.    , 0.    , 0.    , 1.0001]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# X 데이터 오차반영\n",
    "A_new = A + 0.0001 * np.eye(4)\n",
    "A_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-06T14:10:08.684106Z",
     "start_time": "2020-09-06T14:10:08.666154Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.99990001, 0.99990001, 0.99990001, 0.99990001])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 계수 추정\n",
    "np.linalg.solve(A_new, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 조건수 확인\n",
    "np.linalg.cond(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-06T14:16:12.228405Z",
     "start_time": "2020-09-06T14:16:12.217431Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.5       , 0.33333333, 0.25      ],\n",
       "       [0.5       , 0.33333333, 0.25      , 0.2       ],\n",
       "       [0.33333333, 0.25      , 0.2       , 0.16666667],\n",
       "       [0.25      , 0.2       , 0.16666667, 0.14285714]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 조건수가 클 때\n",
    "# X 데이터\n",
    "from scipy.linalg import hilbert\n",
    "A = hilbert(4)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-06T14:12:06.462582Z",
     "start_time": "2020-09-06T14:12:06.446618Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1.])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Y 데이터\n",
    "Y = np.ones(4)\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-06T14:12:15.854297Z",
     "start_time": "2020-09-06T14:12:15.848310Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  -4.,   60., -180.,  140.])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 계수 추정\n",
    "np.linalg.solve(A, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-06T14:12:38.425972Z",
     "start_time": "2020-09-06T14:12:38.407021Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.0001    , 0.5       , 0.33333333, 0.25      ],\n",
       "       [0.5       , 0.33343333, 0.25      , 0.2       ],\n",
       "       [0.33333333, 0.25      , 0.2001    , 0.16666667],\n",
       "       [0.25      , 0.2       , 0.16666667, 0.14295714]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# X 데이터 오차반영\n",
    "A_new = A + 0.0001 * np.eye(4)\n",
    "A_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-06T14:13:01.465242Z",
     "start_time": "2020-09-06T14:13:01.451285Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -0.58897672,  21.1225671 , -85.75912499,  78.45650825])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 계수 추정\n",
    "np.linalg.solve(A_new, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-06T14:16:15.637957Z",
     "start_time": "2020-09-06T14:16:15.594103Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15513.738738929038"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 조건수 확인\n",
    "np.linalg.cond(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- **조건수 감소 방법(분석 결과 안정성 확보 방법):** \n",
    "    > **1) 변수들의 단위차이로 숫자의 스케일들이 크게 다른 경우, 스케일링(Scaling)으로 해결 가능**  \n",
    "    > **2) 독립변수들 간에 상관관계가 높은 \"다중공선성\" 존재할 경우,  \n",
    "    Variance Inflation Factor(VIF)나 Principal Component Analysis(PCA)를 통한 변수선별로 해결 가능**  \n",
    "    > **3) 독립변수들 간 의존성이 높은 변수들에 패널티를 부여하는 정규화(Resularization)로 해결 가능**  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 변수간 스케일 차이 조정(Scaling)\n",
    "\n",
    "- **목적:**\n",
    "    - **(하드웨어)**  \n",
    "    : PC 메모리를 고려하여 오버플로우(Overflow)나 언더플로우(Underflow)를 방지 \n",
    "    - **(소프트웨어)**  \n",
    "    : 독립 변수의 공분산 행렬 조건수(Condition Number)를 감소시켜 최적화 안정성 및 수렴 속도 향상 \n",
    "\n",
    "**1) Standard Scaler:** <center>$\\dfrac{X_{it} - E(X_i)}{SD(X_i)}$</center>\n",
    "> 기본 스케일로 평균을 제외하고 표준편차를 나누어 변환  \n",
    "> 각 변수(Feature)가 정규분포를 따른다는 가정이기에 정규분포가 아닐 시 최선이 아닐 수 있음  \n",
    "\n",
    "<center><img src='Image/Scaling_StandardScaler.png' width='500'></center>\n",
    "\n",
    "~~~\n",
    "sklearn.preprocessing.StandardScaler().fit()\n",
    "sklearn.preprocessing.StandardScaler().transform()\n",
    "sklearn.preprocessing.StandardScaler().fit_transform()\n",
    "~~~\n",
    "\n",
    "**2) Min-Max Scaler:** <center>$\\dfrac{X_{it} - min(X_i)}{max(X_i) - min(X_i)}$</center>\n",
    "> 가장 많이 활용되는 알고리즘으로 최소\\~최대 값이 0\\~1 또는 -1\\~1 사이의 값으로 변환  \n",
    "> 각 변수(Feature)가 정규분포가 아니거나 표준편차가 매우 작을 때 효과적  \n",
    "\n",
    "<center><img src='Image/Scaling_MinMaxScaler.png' width='500'></center>\n",
    "\n",
    "~~~\n",
    "sklearn.preprocessing.MinMaxScaler().fit()\n",
    "sklearn.preprocessing.MinMaxScaler().transform()\n",
    "sklearn.preprocessing.MinMaxScaler().fit_transform()\n",
    "~~~\n",
    "\n",
    "**3) Robust Scaler:** <center>$\\dfrac{X_{it} - Q_1(X_i)}{Q_3(X_i) - Q_1(X_i)}$</center>\n",
    "> 최소-최대 스케일러와 유사하지만 최소/최대 대신에 IQR(Interquartile Range) 중 25%값/75%값을 사용하여 변환  \n",
    "> 이상치(Outlier)에 영향을 최소화하였기에 이상치가 있는 데이터에 효과적이고 적은 데이터에도 효과적인 편  \n",
    "\n",
    "<center><img src='Image/Scaling_RobustScaler.png' width='500'></center>\n",
    "\n",
    "~~~\n",
    "sklearn.preprocessing.RobustScaler().fit()\n",
    "sklearn.preprocessing.RobustScaler().transform()\n",
    "sklearn.preprocessing.RobustScaler().fit_transform()\n",
    "~~~\n",
    "\n",
    "**4) Normalizer:** <center>$\\dfrac{X_{it}}{\\sqrt{X_{i}^2 + X_{j}^2 + ... + X_{k}^2}}$</center>\n",
    "> 각 변수(Feature)를 전체 $n$개 모든 변수들의 크기들로 나누어서 변환(by Cartesian Coordinates)  \n",
    "> 각 변수들의 값은 원점으로부터 반지름 1만큼 떨어진 범위 내로 변환  \n",
    "\n",
    "<center><img src='Image/Scaling_Normalizer.png' width='500'></center>\n",
    "\n",
    "~~~\n",
    "sklearn.preprocessing.Normalizer().fit()\n",
    "sklearn.preprocessing.Normalizer().transform()\n",
    "sklearn.preprocessing.Normalizer().fit_transform()\n",
    "~~~\n",
    "\n",
    "- [**비교 예시**](https://scikit-learn.org/stable/auto_examples/preprocessing/plot_all_scaling.html#sphx-glr-download-auto-examples-preprocessing-plot-all-scaling-py)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 다중공선성(Multicollinearity) 제거\n",
    "\n",
    "- **다중공선성(Multicollinearity) 발생:** \n",
    "\n",
    "    - 독립변수의 일부가 다른 독립변수의 조합으로 표현될 수 있는 경우 \n",
    "    - 독립변수들이 서로 독립이 아니라 상호상관관계가 강한 경우 \n",
    "    - 독립변수의 공분산 행렬(Covariance Matrix) 벡터공간(Vector Space)의 차원과 독립변수의 차원이 같지 않는 경우(Full Rank가 아니다) \n",
    "\n",
    "> **=> \"다중공선성이 있으면 독립변수 공분산 행렬의 조건수(Condition Number)가 증가\"**  \n",
    "> **=> \"조건수(Condition Number)가 증가하면 분석결과 과적합(Overfitting)이 발생할 가능성 증가\"**  \n",
    "\n",
    "- **Variance Inflation Factor(VIF) 변수선택**\n",
    "> **\"VIF는 독립변수를 다른 독립변수들로 선형회귀한 성능을 의미하며, 이를 통해 상호 가장 의존적인 독립변수를 제거\"**  \n",
    "> : 의존성이 낮은(분산이 작은) 독립변수들을 선택하거나, 의존성이 높은(분산이 높은) 독립변수들을 제거할 수 있음\n",
    "\n",
    "<center>\n",
    "$VIF_i = Var(\\hat{\\beta}_i) = \\dfrac{\\sigma^2_{\\epsilon}}{(n-1)Var(X_i)} \\cdot \\dfrac{1}{1-R_i^2} \\\\\n",
    "(R_i^2:~독립변수~X_i를~다른~독립변수들로~선형회귀한~성능(결정계수))$\n",
    "</center>  \n",
    "\n",
    "- **Principal Component Analysis(PCA) 변수선택**\n",
    "> **\"PCA는 다차원인 독립변수 행렬을 서로 독립인 소차원의 독립변수 행렬로 바꾸는 알고리즘으로, 이를 통해 상호 의존성을 제거\"**\n",
    "\n",
    "<center><img src='Image/PCA.PNG' width='350'></center>\n",
    "\n",
    "<center><img src='Image/PCA_Visual.png' width='600'></center>\n",
    "\n",
    "<center><img src='Image/PCA_Visualization.png' width='600'></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 모델링 방향"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [정상성(Stationarity Process)](https://en.wikipedia.org/wiki/Stationary_process)\n",
    "\n",
    "- **시계열이 정상성이다:** 시간의 흐름에 따라 \"통계적 특성(Statistical Properties)\"이 변하지 않음\n",
    "    - **통계적 특성(Statistical Properties):** 주로 평균(Mean)과 분산(Variance)/공분산(Covariance)를 얘기하지만 이를 포함한 모든 분포적 특성을 총칭함\n",
    "    - **[Homoscedasticity](https://en.wikipedia.org/wiki/Homoscedasticity)**: 일정한(유한한, 발산하지않는) 분산을 가짐을 의미 $\\leftrightarrow$ **[Heteroscedasticity](https://en.wikipedia.org/wiki/Heteroscedasticity)**: 발산하는 분산을 가짐을 의미\n",
    "\n",
    "<center><img src='Image/Stationary(on).png' width='300'></center>\n",
    "<center><img src='Image/Stationary(non).png' width='700'></center>\n",
    "\n",
    "- **약정상(Weak Stationarity, Wide-sense Stationary Process):**\n",
    "\n",
    "    - **(비수학적 이해)**  \n",
    "    if $\\{X_{it}\\}^{t=+\\infty}_{t=-\\infty}$ is a weak stationary process,  \n",
    "    1) $X_{i1}$, $X_{i2}$, $X_{i3}$, ... have the same distribution.  \n",
    "    2) $(X_{i1}, X_{i3})$, $(X_{i5}, X_{i7})$, $(X_{i9}, X_{i11})$, ... have the same joint distribution. That's it.  \n",
    "    \n",
    "    - **(수학적 이해)**  \n",
    "    if $\\{X_{it}\\}^{t=+\\infty}_{t=-\\infty}$ is a weak stationary process,  \n",
    "    1) $E(X_{it}) = \\mu$, for all time $t$ (The first moment estimation)  \n",
    "    2) $Var(X_{it}) = E(X_{it}^2) - E(X_{it})^2 < \\infty$, for all time $t$ (The second moment estimation)  \n",
    "    3) $Cov(X_{is}, X_{ik}) = Cov(X_{i(s+h)}, X_{i(k+h)}) = f(h)$, for all time $s, k, h$ (The cross moment estimation)  \n",
    "    => covariance just depends on $h$.  \n",
    "\n",
    "\n",
    "- **강정상(Strong Stationarity, Strictly Stationary Process):**  \n",
    "> **\"확률과정의 모든 분포 모멘트(Moment)가 시간 차이에만 의존하는 것(절대시간 미의존)\"**    \n",
    "\n",
    "    - **(비수학적 이해)**  \n",
    "    if $\\{X_{it}\\}^{t=+\\infty}_{t=-\\infty}$ is a strong stationary process,  \n",
    "    1) $X_{i1}$, $X_{i2}$, $X_{i3}$, ... have the same distribution.  \n",
    "    2) $(X_{i1}, X_{i3})$, $(X_{i5}, X_{i7})$, $(X_{i9}, X_{i11})$, ... have the same joint distribution.  \n",
    "    3) $(X_{i1}, X_{i3}, X_{i5})$, $(X_{i7}, X_{i9}, X_{i11})$, $(X_{i13}, X_{i15}, X_{i17})$, ... must have the same joint distribution.  \n",
    "    4) $(X_{i1}, X_{i3}, ... , X_{i\\infty})$ is invariant under all time translation.  \n",
    "    \n",
    "    - **백색잡음(White Noise, $WN$): <U>강정상 예시로 시계열분석 기본알고리즘 중 가장 중요함</U>**    \n",
    "    <center><img src='Image/White_Noise.png' width='300'></center>\n",
    "    \n",
    "    >**1) 잔차들은 정규분포이고, (unbiased) 평균 0과 일정한 분산을 가져야 함:**  \n",
    "    \\begin{align*}\n",
    "    \\{\\epsilon_t : t = \\dots, -2, -1, 0, 1, 2, \\dots\\} \\sim N(0,\\sigma^2_{\\epsilon_t}) \\\\\n",
    "    \\end{align*}\n",
    "    \\begin{align*}\n",
    "    where~~ \\epsilon_t \\sim  i.i.d(independent~and~identically~distributed) \\\\\n",
    "    \\end{align*}\n",
    "    \\begin{align*}\n",
    "    \\epsilon_t = Y_t - \\hat{Y_t}, \\;\\; E(\\epsilon_t) = 0, \\;\\; Var(\\epsilon_t) = \\sigma^2_{\\epsilon_t} \\\\\n",
    "    \\end{align*}\n",
    "    \\begin{align*}\n",
    "    Cov(\\epsilon_s, \\epsilon_k) = 0~for~different~times!(s \\ne k)\n",
    "    \\end{align*}\n",
    "\n",
    "    >**2) 잔차들이 시간의 흐름에 따라 상관성이 없어야 함:**  \n",
    "        - 자기상관함수(Autocorrelation Fundtion([ACF](https://en.wikipedia.org/wiki/Autocorrelation)))를 통해 $Autocorrelation~=~0$인지 확인\n",
    "            - 공분산(Covariance): \n",
    "            <center>$Cov(Y_s, Y_k)$ = $E[(Y_s-E(Y_s))$$(Y_k-E(Y_k))]$ = $\\gamma_{s,k}$</center>\n",
    "            - 자기상관함수(Autocorrelation Function): \n",
    "            <center>$Corr(Y_s, Y_k)$ = $\\dfrac{Cov(Y_s, Y_k)}{\\sqrt{Var(Y_s)Var(Y_k)}}$ = $\\dfrac{\\gamma_{s,k}}{\\sqrt{\\gamma_s \\gamma_k}}$</center>\n",
    "            - 편자기상관함수(Partial Autocorrelation Function): $s$와 $k$사이의 상관성을 제거한 자기상관함수\n",
    "            <center>$Corr[(Y_s-\\hat{Y}_s, Y_{s-t}-\\hat{Y}_{s-t})]$  for $1<t<k$</center>\n",
    "      \n",
    "- **강정상과 약정상 관계:**\n",
    "> **\"약정상 $\\{x_{it}\\}^{t=+\\infty}_{t=-\\infty}$가 3차 이상의 모멘텀(Skewness, Kurtosis 등)에서도 시간에따라 일정하면, $\\{x_{it}\\}^{t=+\\infty}_{t=-\\infty}$는 강정상이다\"**  \n",
    "> **강정상 $\\{x_{it}\\}^{t=+\\infty}_{t=-\\infty}$의 특정 샘플 $\\{x_{it}\\}^{t={i_2}}_{t={i_1}}$는 평균과 분산까지만 일정한 약정상 일 수 있다**  \n",
    "> **\"강정상 $\\Rightarrow$ 약정상, but 약정상 $\\nRightarrow$ 강정상\"**  \n",
    "\n",
    "\n",
    "- **비정상 확률과정(Non-stationary Process):**  \n",
    "    - 추세가 있어서 일차 모멘트($E(y_t)$)가 0이 아니며 시간에 따라 변화함\n",
    "    - 추세가 없지만($E(y_t) = 0$) 이차 모멘트($Var(y_t)$)가 시간에 따라 변화함\n",
    "    - **랜덤 워크(Random Walk):** 비정상(Non-stationary) 데이터 예시, 차분시 백색잡음(정상성) 전환\n",
    "    <center>$Y_{it} = Y_{it-1} + \\epsilon_t \\\\ Y_{it} - Y_{it-1} = \\epsilon_t \\\\ \\epsilon_t \\sim WN(0,\\sigma_{\\epsilon_t}^2)$</center>\n",
    "  \n",
    "<center><img src='Image/Random_Walk.png' width='400'></center>\n",
    "\n",
    "\n",
    "- **활용주요목적:**  \n",
    "    1) 시계열 모형은 데이터가 Stationary라 가정한다 => Stationary여야 분석 효과가 높다  \n",
    "    2) 백색잡음 또한 Stationary이다 => 잔차검증 역시 Stationary 가정을 전재로 한다  \n",
    "  \n",
    "  \n",
    "- **활용단어예시:**  \n",
    "    - Stationary Process: 정상성인 시계열데이터를 발생시키는 데이터셋(프로세스)\n",
    "    - Stationary Model: 정상성인 시계열데이터를 설명하는 모델\n",
    "    - Trend Stationary: 트랜드를 제거하면 정상성인 시계열데이터\n",
    "    - Seasonal Stationary: 계절성을 제거하면 정상성인 시계열데이터\n",
    "    - Difference Stationary: 차분을하면 정상성인 시계열데이터\n",
    "    - Strictly Stationary: 시간 흐름에 따라 \"통계적 특성\"이 변하지 않음"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-09T14:11:21.823237Z",
     "start_time": "2020-09-09T14:11:20.383089Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 라이브러리 호출\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "from random import seed, random\n",
    "import matplotlib.pyplot as plt\n",
    "%reload_ext autoreload\n",
    "%autoreload 2\n",
    "from module import stationarity_adf_test, stationarity_kpss_test\n",
    "\n",
    "# 랜덤워크 데이터 생성 및 통계량 Test (rho=0)\n",
    "plt.figure(figsize=(10, 4))\n",
    "seed(1)\n",
    "rho = 0\n",
    "random_walk = [-1 if random() < 0.5 else 1]\n",
    "for i in range(1, 1000):\n",
    "    movement = -1 if random() < 0.5 else 1\n",
    "    value = rho * random_walk[i-1] + movement\n",
    "    random_walk.append(value)\n",
    "plt.plot(random_walk)\n",
    "plt.title('Rho: {}\\n ADF p-value: {}'.format(rho, np.ravel(stationarity_adf_test(random_walk, []))[1]))\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# 랜덤워크 데이터 생성 및 통계량 Test (rho=0.6)\n",
    "plt.figure(figsize=(10, 4))\n",
    "seed(1)\n",
    "rho = 0.6\n",
    "random_walk = [-1 if random() < 0.5 else 1]\n",
    "for i in range(1, 1000):\n",
    "    movement = -1 if random() < 0.5 else 1\n",
    "    value = rho * random_walk[i-1] + movement\n",
    "    random_walk.append(value)\n",
    "plt.plot(random_walk)\n",
    "plt.title('Rho: {}\\n ADF p-value: {}'.format(rho, np.ravel(stationarity_adf_test(random_walk, []))[1]))\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# 랜덤워크 데이터 생성 및 통계량 Test (rho=0.9)\n",
    "plt.figure(figsize=(10, 4))\n",
    "seed(1)\n",
    "rho = 0.9\n",
    "random_walk = [-1 if random() < 0.5 else 1]\n",
    "for i in range(1, 1000):\n",
    "    movement = -1 if random() < 0.5 else 1\n",
    "    value = rho * random_walk[i-1] + movement\n",
    "    random_walk.append(value)\n",
    "plt.plot(random_walk)\n",
    "plt.title('Rho: {}\\n ADF p-value: {}'.format(rho, np.ravel(stationarity_adf_test(random_walk, []))[1]))\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# 랜덤워크 데이터 생성 및 통계량 Test (rho=1)\n",
    "plt.figure(figsize=(10, 4))\n",
    "seed(1)\n",
    "rho = 1\n",
    "random_walk = [-1 if random() < 0.5 else 1]\n",
    "for i in range(1, 1000):\n",
    "    movement = -1 if random() < 0.5 else 1\n",
    "    value = rho * random_walk[i-1] + movement\n",
    "    random_walk.append(value)\n",
    "plt.plot(random_walk)\n",
    "plt.title('Rho: {}\\n ADF p-value: {}'.format(rho, np.ravel(stationarity_adf_test(random_walk, []))[1]))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 계수가 1에 가가울수록 시계열 데이터는 평균에서 벗어나는 경향을 보임\n",
    "- 데이터의 계수가 1에 가까운지(있는지 없는지)를 체크하는 통계량 등장: Augmented Dickey-Fuller Test\n",
    "- 1일 경우 단위근이 있다 표현하며, 단위근을 제거하기 위해 차분하면 WN인 정상 데이터로 변환되는 수학형태임"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 정상성 테스트(Stationarity Test)\n",
    "\n",
    "**1) 시각화 테스트(by Visual):** 트랜드와 계절성이 없는지를 파악하여 안정성 확인  \n",
    "<center><img src='Image/Stationary_Visual.png' width='500'></center>\n",
    "\n",
    "**2) 기초통계 테스트(by Summary Statistics):** 특정시간(ex. 계절)에 따른 기초통계가 랜덤한지 파악하여 안정성 확인  \n",
    "**3) 검정통계량 테스트(by Statistical Statistics Test):** 정상성을 테스트하는 검정통계량을 통해 안정성 가설 확인  \n",
    "\n",
    "> [**\"In statistics, a unit root test tests whether a time series variable is non-stationary and possesses a unit root.\"**](https://en.wikipedia.org/wiki/Unit_root_test)\n",
    "\n",
    "- [**Augmented Dickey-Fuller(ADF) test:**](https://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test)\n",
    "    - **가설확인**\n",
    "        - **대중주장(귀무가설, Null Hypothesis, $H_0$):** 시계열 데이터는 단위근(Unit Root)를 있다 / 비정상 상태이다 / 시간의존 구조이다\n",
    "        - **나의주장(대립가설, Alternative Hypothesis, $H_1$):** 시계열 데이터는 단위근이 없다 / 정상 상태이다 / 시간의존 구조가 아니다\n",
    "    - **의사결정**\n",
    "        - **p-value >= 내기준(ex. 0.05):** 내가 수집한(분석한) 시계열 데이터가 대중주장과 유사하기 때문에 대중주장 참 & 나의주장 거짓\n",
    "        > **수집한(분석한) 시계열 데이터는 단위근이 있다 / 비정상 상태이다 / 시간의존 구조이다**\n",
    "        - **p-value < 내기준(ex. 0.05):** 내가 수집한(분석한) 시계열 데이터가 대중주장을 벗어나기 때문에 대중주장 거짓 & 나의주장 참\n",
    "        > **수집한(분석한) 시계열 데이터는 단위근이 없다 / 정상 상태이다 / 시간의존 구조가 아니다**\n",
    "      \n",
    "- [**ADF-GLS test:**](https://en.wikipedia.org/wiki/ADF-GLS_test)  \n",
    "    - **가설확인:** ADF와 동일\n",
    "  \n",
    "- [**Phillips–Perron(PP) test:**](https://en.wikipedia.org/wiki/Phillips%E2%80%93Perron_test)  \n",
    "    - **가설확인:** ADF와 동일\n",
    "  \n",
    "- [**Kwiatkowski Phillips Schmidt Shin(KPSS) test:**](https://en.wikipedia.org/wiki/Phillips%E2%80%93Perron_test)  \n",
    "    - **가설확인:** ADF와 **반대**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 검증지표 방향"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 성능비교를 위한 대표적 검증지표(Metrics)\n",
    "\n",
    "- **R-squared(R^2):** 추정된 (선형)모형이 주어진 데이터에 잘 적합된 정도, 계량경제학에서는 모델에 의해 설명되는 데이터 분산의 정도(퍼센트), $(- \\infty, 1]$  \n",
    "<center>$R^2$ = $\\dfrac{ESS}{TSS}$ = $\\dfrac{\\sum_{i=1}^{n} (\\hat{y}_i - \\bar{y})^2}{\\sum_{i=1}^{n} (y_i - \\bar{y})^2}$ = $1 - \\dfrac{RSS}{TSS}$ = $1 - \\dfrac{\\sum_{i=1}^{n} (y_i - \\hat{y}_i)^2}{\\sum_{i=1}^{n} (y_i - \\bar{y})^2}$</center>\n",
    "\n",
    "~~~\n",
    "sklearn.metrics.r2_score\n",
    "~~~\n",
    "\n",
    "- **Mean Absolute Error(MAE):** 각 데이터의 단위를 보존하는 성능지표, $[0, +\\infty)$\n",
    "<center>$MAE = \\dfrac{1}{n}$ $\\sum\\limits_{i=1}^{n} |y_i - \\hat{y}_i|$</center>\n",
    "\n",
    "~~~\n",
    "sklearn.metrics.mean_absolute_error\n",
    "~~~\n",
    "\n",
    "- **Mean Squared Error(MSE):** 가장 많이 사용되며 큰 오차에 패널티(Penalty)를 높게 부여하는 성능지표, $[0, +\\infty)$  \n",
    "<center>$MSE = \\dfrac{1}{n}$ $\\sum\\limits_{i=1}^{n} (y_i - \\hat{y}_i)^2$</center>\n",
    "\n",
    "~~~\n",
    "sklearn.metrics.mean_squared_error\n",
    "~~~\n",
    "\n",
    "- **Mean Squared Logarithmic Error(MSLE):** MSE와 유사하나 큰값/작은값에 적은/많은 비중(Weignt)을 부여하는 성능지표, Exponential 추세가 있는 데이터에 많이 활용, $[0, +\\infty)$  \n",
    "<center>$MSLE = \\dfrac{1}{n}$ $\\sum\\limits_{i=1}^{n} (log(1+y_i) - log(1+\\hat{y}_i))^2$</center>\n",
    "\n",
    "~~~\n",
    "sklearn.metrics.mean_squared_log_error\n",
    "~~~\n",
    "\n",
    "- **Median Absolute Error(MedAE):** 이상치에 영향을 받지 않는(Robust) 성능지표, $[0, +\\infty)$\n",
    "<center>$MedAE = median(|y_1 - \\hat{y}_1|, |y_2 - \\hat{y}_2|, ... , |y_n - \\hat{y}_n|)$</center>\n",
    "\n",
    "~~~\n",
    "sklearn.metrics.median_absolute_error\n",
    "~~~\n",
    "\n",
    "- **Root Mean Squared Error(RMSE):** MSE의 제곱값을 보정한 성능지표, $[0, +\\infty)$  \n",
    "<center>$RMSE = \\sqrt{MSE}$</center>\n",
    "\n",
    "- **Mean Absolute Percentage Error(MAPE):** MAE와 유사하나 퍼센트 형식으로 표시한 성능지표, $[0, +\\infty)$\n",
    "<center>$MAPE = \\dfrac{100}{n}$ $\\sum\\limits_{i=1}^{n} \\dfrac{|y_i - \\hat{y}_i|}{y_i}$</center>\n",
    "\n",
    "- **Mean Percentage Error(MPE):** MAPE와 유사하나 오차의 부호(+/-)까지 고려한 성능지표, $(-\\infty, +\\infty)$\n",
    "<center>$MPE = \\dfrac{100}{n}$ $\\sum\\limits_{i=1}^{n} \\dfrac{y_i - \\hat{y}_i}{y_i}$</center>\n",
    "\n",
    "- **Summary:**\n",
    "\n",
    "| Acroynm | Full Name | Residual Operation? | Robust To Outliers? |\n",
    "|---------|--------------------------------|---------------------|---------------------|\n",
    "| MAE | Mean Absolute Error | Absolute Value | Yes |\n",
    "| MSE | Mean Squared Error | Square | No |\n",
    "| MedAE | Median Absolute Error | Absolute Value | Yes |\n",
    "| RMSE | Root Mean Squared Error | Square | No |\n",
    "| MAPE | Mean Absolute Percentage Error | Absolute Value | Yes |\n",
    "| MPE | Mean Percentage Error | N/A | Yes |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 검증 유의점(Underfitting vs Overfitting)\n",
    "- **과소적합(Underfitting):** 단순모델 또는 높은편향(충분하지 않은 데이터패턴 학습)\n",
    "- **과적합(Overfitting):** 복잡한모델 또는 높은분산(주어진 데이터패턴에만 효과)\n",
    "    - **발생:** 같은 조건에 대해 추정되는 답이 복수개 존재할 수 있는 상황\n",
    "        - 독립변수 갯수에 비해 추정해야 할 파라미터/모수의 수가 과도하게 큰 경우  \n",
    "        - 독립변수가 서로 독립이 아닌 경우  \n",
    "    - **문제이유:**\n",
    "        - 학습에 사용되지 않는 새로운 독립변수 값을 입력하면 오차가 커짐 (Cross-validation 오차)\n",
    "        - 샘플 데이터가 조금만 변화해도 추정되는 파라미터/모수의 값이 크게 달라짐 (추정의 불안정성/부정확성)\n",
    "\n",
    "<center><img src='Image/Underfitting_Overfitting.jpg' width='600'></center>\n",
    "<center><img src='Image/Underfitting_Overfitting.png' width='600'></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 편향-분산 상충관계(Bias-variance Trade-off)  \n",
    "\n",
    "**1) 편향과 분산의 정의**\n",
    "> **(비수학적 이해)**\n",
    "- **편향(Bias):** 점추정  \n",
    "    - 예측값과 실제값의 차이  \n",
    "    - 모델 학습시 여러 데이터로 학습 후 예측값의 범위가 정답과 얼마나 멀리 있는지 측정  \n",
    "- **편향(Bias(Real)):** 모형화(단순화)로 미처 반영하지 못한 복잡성  \n",
    "    <U>=> 편향이 작다면 Training 데이터 패턴(복잡성)을 최대반영 의미</U>  \n",
    "    <U>=> 편향이 크다면 Training 데이터 패턴(복잡성)을 최소반영 의미</U>  \n",
    "- **분산(Variance):** 구간추정  \n",
    "    - 학습한 모델의 예측값이 평균으로부터 퍼진 정도(변동성/분산)  \n",
    "    - 여러 모델로 학습을 반복한다면, 학습된 모델별로 예측한 값들의 차이를 측정\n",
    "- **분산(Variance(Real)):** 다른 데이터(Testing)를 사용했을때 발생할 변화  \n",
    "    <U>=> 분산이 작다면 다른 데이터로 예측시 적은 변동 예상</U>  \n",
    "    <U>=> 분산이 크다면 다른 데이터로 예측시 많은 변동 예상</U>  \n",
    "    \n",
    "<center><img src='Image/Bias_Variance1.jpeg' width='400'></center>\n",
    "\n",
    "> **(수학적 이해)**\n",
    "\n",
    "\\begin{align*}\n",
    "\\text{Equation of Error} && Err(x) &= E\\Bigl[\\bigl(Y-\\hat{f}(x)\\bigr)^2 \\Bigr] \\\\\n",
    "&& &= \\Bigl(E[\\hat{f}(x)] - f(x)\\Bigr)^2 + E \\Bigl[\\bigl(\\hat{f}(x) - E[\\hat{f}(x)]\\bigr)^2 \\Bigr] + \\sigma_{\\epsilon}^2 \\\\\n",
    "&& &= \\text{Bias}^2 + \\text{Variance} + \\text{Irreducible Error}\n",
    "\\end{align*}\n",
    "\n",
    "**2) 편향과 분산의 관계**\n",
    "- **모델의 복잡도가 낮으면 Bias가 증가하고 Variance가 감소(Underfitting)**  \n",
    ": 구간추정 범위는 좁으나 점추정 정확성 낮음  \n",
    ": Training/Testing 모두 예측력이 낮음\n",
    "- **모델의 복잡도가 높으면 Bias가 감소하고 Variance가 증가(Overfitting)**  \n",
    ": 점추정 정확성은 높으나 구간추정 범위는 넓음  \n",
    ": Training만 잘 예측력 높고 Testing은 예측력 낮음  \n",
    "- **Bias와 Variance가 최소화 되는 수준에서 모델의 복잡도 선택**  \n",
    "\n",
    "<center><img src='Image/Bias-Variance-Tradeoff.png' width='400'></center>\n",
    "<center><img src='Image/Bias_Variance4.png' width='400'></center>\n",
    "\n",
    "**3) 편향과 분산 모두를 최소화하는 방법**\n",
    "<center><img src='Image/Bias_Variance_Reduce.png' width='600'></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 잔차진단 방향\n",
    "> **\"모델링이 데이터의 패턴을 최대한 반영했을 경우 분석을 마무리 해도 좋다\"**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [정상성 테스트](https://en.wikipedia.org/wiki/Unit_root_test)\n",
    "\n",
    "- [**Augmented Dickey-Fuller(ADF) test:**](https://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test)\n",
    "    - **가설확인**\n",
    "        - **대중주장(귀무가설, Null Hypothesis, $H_0$):** 시계열 데이터는 단위근(Unit Root)를 있다 / 비정상 상태이다 / 시간의존 구조이다\n",
    "        - **나의주장(대립가설, Alternative Hypothesis, $H_1$):** 시계열 데이터는 단위근이 없다 / 정상 상태이다 / 시간의존 구조가 아니다\n",
    "    - **의사결정**\n",
    "        - **p-value >= 내기준(ex. 0.05):** 내가 수집한(분석한) 시계열 데이터가 대중주장과 유사하기 때문에 대중주장 참 & 나의주장 거짓\n",
    "        > **수집한(분석한) 시계열 데이터는 단위근이 있다 / 비정상 상태이다 / 시간의존 구조이다**\n",
    "        - **p-value < 내기준(ex. 0.05):** 내가 수집한(분석한) 시계열 데이터가 대중주장을 벗어나기 때문에 대중주장 거짓 & 나의주장 참\n",
    "        > **수집한(분석한) 시계열 데이터는 단위근이 없다 / 정상 상태이다 / 시간의존 구조가 아니다**\n",
    "      \n",
    "- [**ADF-GLS test:**](https://en.wikipedia.org/wiki/ADF-GLS_test)  \n",
    "    - **가설확인:** ADF와 동일\n",
    "  \n",
    "- [**Phillips–Perron(PP) test:**](https://en.wikipedia.org/wiki/Phillips%E2%80%93Perron_test)  \n",
    "    - **가설확인:** ADF와 동일\n",
    "  \n",
    "- [**Kwiatkowski Phillips Schmidt Shin(KPSS) test:**](https://en.wikipedia.org/wiki/Phillips%E2%80%93Perron_test)  \n",
    "    - **가설확인:** ADF와 **반대**\n",
    "\n",
    "\n",
    "- **예시:**\n",
    "\n",
    "<center><img src='Image/ADF_example1.png' width='600'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/ADF_example2.png' width='300'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/ADF_example3.png' width='600'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/ADF_example4.png' width='600'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/ADF_example5.png' width='600'></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [정규분포 테스트(Normality Test)](https://en.wikipedia.org/wiki/Normality_test)\n",
    "\n",
    "- [**Shapiro–Wilk test:**](https://en.wikipedia.org/wiki/Shapiro%E2%80%93Wilk_test)\n",
    "    - **가설확인**\n",
    "        - **대중주장(귀무가설, Null Hypothesis, $H_0$):** 데이터는 정규분포 형태이다\n",
    "        - **나의주장(대립가설, Alternative Hypothesis, $H_1$):** 데이터는 정규분포가 아닌 형태다\n",
    "    - **의사결정**\n",
    "        - **p-value >= 내기준(ex. 0.05):** 내가 수집한(분석한) 데이터가 대중주장과 유사하기 때문에 대중주장 참 & 나의주장 거짓\n",
    "        > 내가 수집한(분석한) 데이터는 정규분포 형태이다\n",
    "        - **p-value < 내기준(ex. 0.05):** 내가 수집한(분석한) 데이터가 대중주장을 벗어나기 때문에 대중주장 거짓 & 나의주장 참\n",
    "        > 내가 수집한(분석한) 데이터는 정규분포가 아닌 형태다\n",
    "\n",
    "- [**Kolmogorov–Smirnov test:**](https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test)\n",
    "    - **가설확인:** Shapiro–Wilk와 동일\n",
    "  \n",
    "- [**Lilliefors test:**](https://en.wikipedia.org/wiki/Lilliefors_test)\n",
    "    - **가설확인:** Shapiro–Wilk와 동일\n",
    "  \n",
    "- [**Anderson–Darling test:**](https://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test)\n",
    "    - **가설확인:** Shapiro–Wilk와 동일\n",
    "  \n",
    "- [**Jarque–Bera test:**](https://en.wikipedia.org/wiki/Jarque%E2%80%93Bera_test)\n",
    "    - **가설확인:** Shapiro–Wilk와 동일\n",
    "  \n",
    "- [**Pearson's chi-squared test:**](https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test)\n",
    "    - **가설확인:** Shapiro–Wilk와 동일\n",
    "  \n",
    "- [**D'Agostino's K-squared test:**](https://en.wikipedia.org/wiki/D%27Agostino%27s_K-squared_test)\n",
    "    - **가설확인:** Shapiro–Wilk와 동일\n",
    "    \n",
    "    \n",
    "- **예시:**\n",
    "\n",
    "<center><img src='Image/SW_example1.png' width='600'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/SW_example2.png' width='300'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/SW_example3.png' width='400'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/SW_example4.png' width='600'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/SW_example5.png' width='600'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/SW_example6.png' width='600'></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 자기상관 테스트(Autocorrelation Test)\n",
    "\n",
    "- [**Ljung–Box test:**](https://en.wikipedia.org/wiki/Ljung%E2%80%93Box_test)\n",
    "    - **가설확인**\n",
    "        - **대중주장(귀무가설, Null Hypothesis, $H_0$):** 시계열 데이터의 Autocorrelation은 0이다(존재하지 않는다)\n",
    "        - **나의주장(대립가설, Alternative Hypothesis, $H_1$):** 시계열 데이터의 Autocorrelation은 0이 아니다(존재한다)\n",
    "    - **의사결정**\n",
    "        - **p-value >= 내기준(ex. 0.05):** 내가 수집한(분석한) 데이터가 대중주장과 유사하기 때문에 대중주장 참 & 나의주장 거짓\n",
    "        > **내가 수집한(분석한) 시계열 데이터의 Autocorrelation은 존재하지 않는다**\n",
    "        - **p-value < 내기준(ex. 0.05):** 내가 수집한(분석한) 데이터가 대중주장을 벗어나기 때문에 대중주장 거짓 & 나의주장 참\n",
    "        > **내가 수집한(분석한) 시계열 데이터의 Autocorrelation은 존재한다**\n",
    "\n",
    "- [**Portmanteau test:**](https://en.wikipedia.org/wiki/Portmanteau_test)\n",
    "    - **가설확인:** Ljung–Box와 동일\n",
    "\n",
    "- [**Breusch–Godfrey test:**](https://en.wikipedia.org/wiki/Breusch%E2%80%93Godfrey_test)\n",
    "    - **가설확인:** Ljung–Box와 동일\n",
    "  \n",
    "- [**Durbin–Watson statistic:**](https://en.wikipedia.org/wiki/Durbin%E2%80%93Watson_statistic)\n",
    "    - **가설확인:** Ljung–Box와 동일\n",
    "    - **의사결정:** 검정통계량 범위 - $[0, 4]$\n",
    "        - **2 근방:** 내가 수집한(분석한) 데이터가 대중주장과 유사하기 때문에 대중주장 참 & 나의주장 거짓\n",
    "        > **내가 수집한(분석한) 시계열 데이터의 Autocorrelation은 존재하지 않는다**\n",
    "        - **0 또는 4 근방:** 내가 수집한(분석한) 데이터가 대중주장을 벗어나기 때문에 대중주장 거짓 & 나의주장 참\n",
    "        > **내가 수집한(분석한) 시계열 데이터의 Autocorrelation은 존재한다**\n",
    "            - 0: 양(Positive)의 Autocorrelation 존재한다\n",
    "            - 4: 음(Negative)의 Autocorrelation 존재한다\n",
    "            \n",
    "            \n",
    "- **예시:**\n",
    "\n",
    "<center><img src='Image/LB_example1.jpg' width='400'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/LB_example2.jpg' width='600'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/DW_example1.png' width='600'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/DW_example2.png' width='300'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/DW_example3.png' width='600'></center>"
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    "### [등분산성 테스트(Homoscedasticity Test)](https://en.wikipedia.org/wiki/Homoscedasticity)\n",
    "\n",
    "- [**Goldfeld–Quandt test:**](https://en.wikipedia.org/wiki/Goldfeld%E2%80%93Quandt_test)\n",
    "    - **가설확인**\n",
    "        - **대중주장(귀무가설, Null Hypothesis, $H_0$):** 시계열 데이터의 Homoscedasticity 상태다(등분산이다)\n",
    "        - **나의주장(대립가설, Alternative Hypothesis, $H_1$):** 시계열 데이터의 Heteroscedasticity 상태다(등분산이 아니다 / 발산하는 분산이다)\n",
    "    - **의사결정**\n",
    "        - **p-value >= 내기준(ex. 0.05):** 내가 수집한(분석한) 데이터가 대중주장과 유사하기 때문에 대중주장 참 & 나의주장 거짓\n",
    "        > **내가 수집한(분석한) 시계열 데이터는 등분산이다**\n",
    "        - **p-value < 내기준(ex. 0.05):** 내가 수집한(분석한) 데이터가 대중주장을 벗어나기 때문에 대중주장 거짓 & 나의주장 참\n",
    "        > **내가 수집한(분석한) 시계열 데이터는 등분산이 아니다**\n",
    "\n",
    "- [**Breusch–Pagan test:**](https://en.wikipedia.org/wiki/Breusch%E2%80%93Pagan_test)\n",
    "    - **가설확인:** Goldfeld–Quandt와 동일\n",
    "\n",
    "- [**Bartlett's test:**](https://en.wikipedia.org/wiki/Bartlett%27s_test)\n",
    "    - **가설확인:** Goldfeld–Quandt와 동일\n",
    "    \n",
    "    \n",
    "- **예시:**\n",
    "\n",
    "<center><img src='Image/GQ_example1.jpg' width='500'></center>\n",
    "\n",
    "---\n",
    "\n",
    "<center><img src='Image/GQ_example2.jpg' width='400'></center>"
   ]
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