State-dependent model, multi-step-ahead, multiple forecasts: Experience with the United States unemployment rate series

This study develops a framework for the fitting, analysis, and forecasting of linear and nonlinear time series models. Through Priestley's State Dependent Model and the Kalman filter algorithm, linear, nonlinear and nonstationary models have been fitted to the US unemployment rate series. The algorithm has been extended to account for both nonlinearity and nonstationarity. Also, some of the existing tests for linearity in the time domain have been applied and indicate the existence of bilinear type nonlinearity in the series. Models fitted in the state dependent framework and the bilinear models have been used for one to twelve step ahead forecasting. The models fitted in the state dependent framework outperform other models, and the bilinear models outperform the linear model. The performance of the existing forecast accuracy comparison tests has been analyzed empirically and through simulation. An alternative to the Diebold and Mariano test has been suggested, which appears to have better size than the Diebold and Mariano test.