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 con- tribute 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.
Weighted forecasts from SETARs with single- and multiple thresholds
Marcella Niglio
2025
Abstract
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 con- tribute 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
