Forecasting the individual components
We have seen how to split a seasonal time series into four components,
Data = Seasonal effect + Trend + Cyclical + Residual
The main benefit from separately identifying the four components is that each of the first three components can be forecast into the future.
Forecast = Seasonal effect + Trend forecast + Cyclical forecast
The three components of the forecast are:
By separately forecasting these three components, we can obtain more accuracy.
Monthly temperatures in Boulder, Colorado
The diagram below again shows the four components of the monthly mean temperature data.
Select the checkbox Seasonal. The seasonal component is removed from the top series and added to the bottom, and is forecast for two years into the future.
De-select Seasonal and select Trend. There is very little trend, but a quadratic trend is forecast into the future in the bottom half of the diagram.
Finally select Cyclical on its own. Since there is minimal autocorrelation, this component is also small, but the cyclical component is now forecast in the bottom half of the diagram.
Finally, select all of Seasonal, Trend and Cyclical. The resulting forecasts in the bottom of the diagram are close to optimum.
Since the trend and autocorrelation are negligible, forecasting temperatures from only the seasonal component would be equally accurate.