Temporal Aggregation

Temporal aggregation transforms a time series into a new time series with a coarser granularity. The goal of aggregation is to filter out patterns, such as seasonal patterns. This is particularly useful when these patterns do not play a role in the required forecast. Filtering out these patterns helps the forecasting algorithm by preventing it from having to identify the filtered structure before making the forecast. Since any pattern derived from data always involves estimation error, pre-filtering irrelevant patterns not only reduces computational time but also improves the accuracy of the result.

The following graphic shows, at the top, the average hourly air temperature over the past 30 years at the weather station in Würzburg. Below, the data for the last two years and the last three days are displayed. These latter graphics illustrate that the hourly temperature time series exhibits a recurring pattern (a seasonality) both within a day and within a year.

A prediction of the average monthly temperature can be made by forecasting the hourly temperatures for all hours of the following month; the monthly forecast is then the average of the individual hourly forecasts.

However, with this approach, the forecasting algorithm must identify both the seasonal pattern shown in the bottom left and the daily pattern shown in the bottom right. The identification of the daily pattern is not necessary for predicting the monthly average. More accurate forecasts typically result when a monthly time series of average temperatures (calculated over each month) is first obtained through temporal aggregation. This is shown in the left part of the following graphic.

The monthly time series contains only the seasonal pattern relevant to forecasting average monthly temperatures; this pattern is more clearly identifiable after aggregation and easier for the forecasting algorithm to quantify. The right part contains the time series aggregated over the average temperatures of a year. This no longer exhibits seasonality. Instead, a trend appears, which is less apparent in the monthly values. The long-term developments identified in this way can be used, especially for long-horizon forecasts, to improve the forecast on a monthly basis.