Using linear and quadratic models for forecasting

Having obtained the equation of a trend line by least squares, forecasting is simply a matter of inserting future time values into the equation.

Predicting credit card debt

The diagram below shows total credit card debt ($millions) in New Zealand at the end of December each year from 1990 to 2001.

The least squares line has been drawn on the time series plot and has been extended 6 years into the future. Drag over the diagram to display the forecasts for these years. (Note that the 'forecasts' for earlier years in which we already have data are the fitted values for the linear model.)

The linear model is a poor fit for these data — the model does not pick up the steeper increase in the last few years of the series. Select Quadratic Model from the pop-up menu and repeat. The quadratic model often gives reasonable forecasts a few years into the future, but you should have some doubts about using this model to predict as far into the future as 2006!

Dangers in forecasting

It is important to realise that the forecasts from linear or quadratic models are highly dependent on the type of line or curve that is chosen for modelling. The dangers are the same as those for extrapolation in bivariate relationships.

Beware forecasting many time periods into the future — the shape of the actual trend line might be different from your model.

Predicting credit card debt

The diagram below also shows the quadratic model based on the data from 1990 to 2001, but adds the actual credit card debt from 2002 to 2013.

Although the trend was close to quadratic up to 2002, a quadratic model does not match the trend further into the future. Quadratic models should not be used to predict more than one or two time periods into the future.