- Forecasting Trend: when a time series evolves slowly and smoothly over time, we say that it shows a trend. (long-term behavior for the entire series e.g. 10 years)
- Forecasting Cycles: when a time series exhibit periodic fluctuations, we say that it has a cycle. (something repeats itself over many years)
- Forecasting Seasonality: a cycle is seasonal when specific fluctuations occur within the calender year, for instance activites that peak in summer months.
- Forecasting with Regression Models (with time-series data)
- Combining Forecasts (competing models)
- Advanced Methods (e.g. ARIMA, GARCH, etc.)
-
A forecast is a statement about the future.
-
We define forecasting as the science and the art to predict a future event with some degree of accuracy.
- In economics, methods of forecasting include:
- Guessing, "rule of thumb", or "informal models"
- Expert judgment
- Extrapolation
- Leading indicators
- Surveys
- Time series models
- Econometric systems
- One of the main problems with forecasting in economics is that economies evolve over time and are subject to intermittent, and sometimes large, unanticipated shocks.
- Some relevant areas:
- Operations planning and control
- Marketing
- Economics
- Financial asset management
- Financial risk management
- ...
-
${y_t }$ entire set of observations -
$y_t$ known value of the series -
$Y_{t+h}$ random variable (future at time t+h) -
$y_{t+h}$ unknown value of the random variable -
$I_t$ univariate / multivariate information set -
$f_{t,1}$ 1-step ahead (tomorrow based on today) -
$f_{t,h}$ h-step ahead () $e_ {t,h}= y_ {t+h} - f_ {t,h}$
- Q: How to find an appropriate model for a Time Series?
- A: There are 3 steps
- Model Specification (or identification)
- Select the types of plausible models given the data
- Model Fitting
- Follow the parsimony principle
- Model Diagnostics
- Assess the quality of the model
- Model Specification (or identification)