This paper introduces the idea of adjusting forecasts from a linear time series model where the adjustment relies on the assumption that this linear model is an approximation of a nonlinear time series model. This way of creating forecasts could be convenient when inference for a nonlinear model is impossible, complicated or unreliable in small samples. The size of the forecast adjustment can be based on the estimation results for the linear model and on other data properties such as the first few moments or autocorrelations.
An illustration is given for a first-order diagonal bilinear time series model, which in certain properties can be approximated by a linear ARMA(1, 1) model. For this case, the forecast adjustment is easy to derive, which is convenient as the particular bilinear model is indeed cumbersome to analyze in practice. An application to a range of inflation series for low-income countries shows that such adjustment can lead to some improved forecasts, although the gain is small for this particular bilinear time series model.

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Econometric Institute Reprint Series
Journal of Forecasting

Franses, P. H. (2018). Model-based forecast adjustment: with an illustration to inflation. Journal of Forecasting. doi:10.1002/for.2557