Abstract: Nonlinear models have been widely employed to characterize the
underlying structure in a time series. It has been shown that the
in-sample fit of nonlinear models is better than linear models, however,
the superiority of nonlinear models over linear models, from the
perspective of out-of-sample forecasting accuracy remains doubtful. We
compare forecast accuracy of nonlinear regime switching models against
classical linear models using different performance scores, such as root
mean square error (RMSE), mean absolute error (MAE), and the continuous
ranked probability score (CRPS). We propose and investigate the efficacy
of a class of simple nonparametric, nonlinear models that are based on
estimation of a few parameters, and can generate more accurate forecasts
when compared with the classical models. Also, given the importance of
gauging uncertainty in forecasts for proper risk assessment and well
informed decision making, we focus on generating and evaluating both point
and density forecasts.
Keywords: Nonlinear, Forecasting, Performance scores.