Weighted forecasts from SETARs with single- and multiple thresholds

We derive an explicit expression for the optimal one-step ahead forecast obtained from fitted self exciting threshold autoregressive (SETAR) models using a weighted average of past observations. The weights, obtained from the minimization of the mean squared forecast error, are analytically derived and the components that contribute to their definition are examined. Based on parameter estimates of single- and multiple threshold SETARs, we show that the new forecast improves the relative forecasting performance of these nonlinear models via a Monte Carlo simulation study. Empirical evidence of the good out-of-sample performance of the new forecast comes from an application to quarterly U.S. real GNP data over the period 1947–2019.