Monday, September 29, 2014

Forecasting and Backcasting

Forecasting is the process of exploring the future events that have not been observed or determined. Backcasting "typically" refers to the process of exploring the past events given the information known to date. The two terms seem to be mutually exclusive, but are often used in an ambiguous way.

Before explaining the two terms in detail, let me briefly go over the basic forecasting terminology:
  • Forecast origin - the last available point in the historical data.
  • Forecast horizon - the distance between the forecast origin and the furthest point we are forecasting.
  • Step - the distance between the two adjacent observations. 
Take day-ahead hourly load forecasting as an example. Usually, the load forecaster need to provide the forecast in the morning, i.e., 6am, for the 24 hours of the next day through hour ending 12am. Let's say the forecaster starts developing the forecast at 5:10 am with hourly weather data and load data through hour ending 5am. Then the forecast origin is 5am of the day. Each step is 1 hour. The forecast horizon is 43 hours or 43 steps. Notice that in practice day-ahead load forecasting is different from 24-hour ahead load forecasting.

There are two types of "forecasting": ex-ante forecasting and ex-post forecasting. Ex-ante forecasting means forecasting with information known through the forecast origin. This is the only way to produce genuine forecasts. Ex ante forecasting is also called "before the event" forecasting, while ex-post forecasting is referred as "after the event" forecasting. In other words, the information of explanatory variables is assumed to be known when producing ex-post forecasts.

Back to the day-ahead load forecasting example, if day-ahead temperature forecasts are used to produce the day-ahead load forecast, the results are ex-ante forecasts. If actual temperatures of the next day are used, the results are ex-post forecasts. Now you probably see an overlap between forecasting and backcasting: ex-post forecasting is a subset of backcasting.

There are several other types of backcasting. One is to fit a model on historical data, which is also called model fitting. Another one is to first dig a hole (or several holes) in the history and then use the rest of the history to estimate the observations in the hole(s) assuming the actual temperatures are known for the entire history. This is similar to cross validation, though cross validation is usually conducted iteratively. (BTW, there will be another post about training, validation and test.) When the hole is at the end of the history, this cross validation becomes ex-post forecasting. Here it comes another overlap between backcasting and forecasting: backcasting is part of the entire forecasting process. To build a model for load forecasting, we usually need to do model fitting, ex-post forecasting, and sometimes, cross validation.

To avoid confusion, I would try not to use the term backcasting unless in the situation of a "one-time" cross validation. In the load forecasting track of Global Energy Forecasting Competition 2012, we named the topic as "forecasting and backcasting electricity demand". The "forecasting" was ex-ante forecasting, because we did not provide temperature data for the forecasted week. The "backcasting" was cross validation, because we dug eight holes in the history and provided actual temperatures for these holes.

Back to Load Forecasting Terminology

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