Correcting for Misspecification in Parameter Dynamics to Improve Forecast Accuracy with Adaptively Estimated Models

Abstract

A daptive estimation methods have become a popular tool for capturing and forecasting changing conditions in dynamic environments. Although adaptive models can provide superior one-step-ahead forecasts, their application to multiperiod forecasting is challenging when the underlying parameter variation process is not correctly specified. The authors propose a methodology based on the Chebyshev approximation method (CAM), which provides a parsimonious substitute for the measurement updating process in the forecasting period, to help forecasters improve multiperiod accuracy in the case of parameter variation misspecification. In two empirical applications concerning the sales growth of new brands, CAM exhibits superior forecasting performance compared to a variety of benchmarks. CAM's properties are further explored through extensive simulations, which suggest that the proposed method is more likely to increase forecast accuracy when parameter variation is more systematic but misspecified because of uncertainty regarding its exact functional form.

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