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:

Seasonal effect
We forecast that the same seasonal effects will hold into the future.
Trend
If the trend is modelled with a linear or quadratic model, any future time can be inserted into the model to obtain a forecast of the trend.
Cyclical
If an autoregressive model is used to model the cyclical component, we can forecast the cyclical component one time period into the future by applying the model to the final deseasonalised, detrended value. The model is then applied sequentially to the forecast to extend it into the future. The cyclical forecasts usually tail away quickly to zero.

By separately forecasting these three components, we can obtain more accuracy.

Tourist arrivals in Fiji

The diagram below again shows the four components of the tourist arrival data from Fiji.

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. The quadratic trend is forecast into the future in the bottom half of the diagram.

Finally select Cyclical on its own. 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.

There was a political coupe d'état in Fiji in 2000. As a result, tourist numbers plummeted and the above forecasts substantially overestimated tourist arrivals in 2000.

Forecasts can never hope to take account of such unpredictable events.