ARIMA-style feed analysis: for {BoxCox=T/F, diff=0,1,2}, plot the seasonality and ACF/PACF

[trentmc]

Background / motivation

Parent epic: #1006 "Explore SARIMAX modeling"

Top-level goal: Help user answer which of which transform to use {0, B0, B1, B2}, to (a) achieve stationarity; and (b) see how well the signal can decompose into trend / seasonal / residual.

Specific transforms:

• 0: differencing = 0
• B0: Box-Cox transform + differencing=0
• B1: Box-Cox transform + differencing=1
• B2: Box-Cox transform + differencing=1

Sub-goals: We want it easy to see these:

• decomposition into trend / seasonal / residual
• relative strengths of trend vs seasonality vs resid
• ACF & PACF. That is, autocorrelation function & partial autocorrelation function, for insight into best AR coefficient etc
• ADF for each transform {0, B0, B1, B2}. Insight: the lowest # that has ADF < 0.05 is the best
• Then, make it easy for the user to select a transform and see the plots ^ for that given transform

Best ref: jahnvisikligar Master's thesis https://github.com/jahnvisikligar/Masters-Thesis/blob/main/Final_Thesis_code.ipynb

TODOs / DoD

• Add real crypto data, ready for use by unit tests PR #1016
• Unit test with plots for each sub-component:
  • decomposition into trend / seasonal / residual PR #1016
  • relative strengths of trend vs seasonality vs resid PR #1025
  • ACF & PACF PR #1026
  • ADF for each transform {0, B0, B1, B2}. (Calc'd it as part of above line. Plots are being done in another issue).

Main prototype: with everything

For a given choice of differencing {0,B0,B1,B2}, show

• 5 decomposition plots: energy per signal, plus 4 signals: (i) observed feed (ii) "trend" (iii) "seasonal", "residual".
• autocorrelation (ACF) & partial autocorrelation (PACF) plots

Other Prototypes & Examples

Prototype: decomposition into trend / seasonality / residual

Prototype: For differencing=0,B0,B1,B2, show 5 decomposition plots

Prototype: For differencing=0,B0,B1,B2, show ACF & PACF

Example 0: neptune.ai "select model"

Ref: neptune.ai select-model post

from statsmodels.tsa.seasonal import seasonal_decompose
result = seasonal_decompose(co2_data)
result.plot()

Example 1a: Sikligar thesis, Differencing=0

Ref: Sikligar thesis & code

Example 1b: Sikligar thesis, Differencing=1

Ref: Sikligar thesis & code

Example 2: neptune.ai catfish sales

result = seasonal_decompose(lim_catfish_sales,model='additive')
fig = result.plot()

Ref: neptune.ai catfish, in this neptune.ai post/py code.

[trentmc]

Seasonal decomposition of Binance BTC/USDT close price Feb 1, 2024 - Mar 8, 2024

[trentmc]

Part 1 done here: #1016

[trentmc]

Results for data: merged_ohlcv_df_BTC-ETH_2024-02-01_to_2024-03-08.csv, using BTC/USDT c 5m.

BoxCox=F, diff=0

BoxCox=T, diff=0

BoxCox=T, diff=1