摘要：Threshold autoregressive (TAR) models can accommodate the asymmetric cycling behavior observed in some time series data. This study develops a procedure to estimate TAR models when the conditional mean of the dependent variable is function of one or more exogenous factors while allowing for heteroskedasticity, i.e. for different levels of variation in upward versus downward cycles. The formulas to obtain predictions from TAR models are derived. Monte Carlo simulation analyses suggest that TAR models can significantly improve forecasting precision. Substantial gains in forecasting precision, in comparison with AR models, are in fact found when applying the proposed procedure to the modeling of U.S. quarterly soybeans future prices and Brazilian coffee spot prices. The estimated TAR models also provide useful insights on the markedly different dynamics of the upward versus the downward cycles exhibited by U.S. soybeans and Brazilian coffee prices.
