Regression Model Forecasting, Scenario based forecasting, Non-Linear Regression Models

Ex-ante / Ex-post forecasting

• Ex-ante forecasts utilize information that is available in advance such as trend, seasonality, or any calendar variables; however, this also suggests that predictors used for the forecast must also be forecasted beforehand.
• Ex-post forecasts utilize later information on predictors; they are more useful for studying the behaviors of forecasting models with the future knowledge of predictors.

Scenario based forecasting

• It is also possible to make forecasts using a regression model while considering specific scenarios that are bound to happen or that are of interest.

• For example, it is possible to make predictions on future changes to the predictors, such as an increasing/decreasing rate of some index.

• The example below shows the forecasts for the electricity demand based on two scenarios that are to happen in the future: a temperature of 35 degrees or 15 degrees.

  

• Note that the prediction intervals for the scenario-based forecasting does not include the uncertainty associated with the predictors itself and it would be more certain if the predictors are distributed closer to the sample mean.

Non-Linear Regression

• Although linear relationships explain many of the real life data, non-linear models are often more suitable for certain scenarios.

• The following plot below represents the annual population of Afganistan throughout the years, where we can see a linear model might not be the most adequate. In fact, there are two knots at this model (1980, 1989), which is when the Soviet-Afgan war occured.

  

• A non-linear, in this case, a piecewise model better explains the recent data and is more capable of making accurate forecasts as seen below.