Model-based forecast adjustment; with an illustration to inflation

This paper introduces the idea to adjust forecasts from a linear time series model where the adjustment relies on the assumption that this linear model is an approximation of for example a nonlinear time series model. This way to create forecasts can be convenient when inference for the 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 like the first few moments or autocorrelations. An illustration is given for an ARMA(1,1) model which is known to approximate a first order diagonal bilinear time series model. For this case, the forecast adjustment is easy to derive, which is convenient as the particular bilinear model is indeed cumbersome to analyze. An application to a range of inflation series for low income countries shows that such adjustment can lead to improved forecasts, although the gain is not large nor frequent