Combined forecasts from linear and nonlinear time series models

Combined forecasts from a linear and a nonlinear model are investigated for time series with possibly nonlinear characteristics. The forecasts are combined by a constant coefficient regression method as well as a time varying method. The time varying method allows for a locally (non)linear modeling. The methods are applied to three data sets: Canadian lynx and sunspot series, US annual macro-economic time series - used by Nelson and Plosser (J. Monetary Econ., 10 (1982) 139) - and US monthly unemployment rate and production indices. It is shown that the combined forecasts perform well, especially with time varying coefficients. This result holds for out of sample performance for the sunspot series, the Canadian lynx number series and the monthly series, but it does not uniformly hold for the Nelson and Plosser economic time series.