Conditional Threshold Autoregression (CoTAR)

Abstract

We propose a new time series model called Conditional Threshold Autoregression (CoTAR), in which the threshold is specified as an empirical quantile of recent observations of a threshold variable. The conditional threshold is expected to trace economic and financial variables well, as a cutoff level of low and high regimes likely changes over time. The presence versus absence of conditional threshold effects can be tested via the wild bootstrap, and the out-of-sample predictive ability of CoTAR can be evaluated via the Diebold-Mariano test. We show that CoTAR satisfies desired statistical properties in both large and small samples. We apply the proposed model to the CBOE Volatility Indices of S&P 500 and major U.S. shares, obtaining desired in-sample and out-of-sample results.

Keywords: profiling estimation, regime switch, self-exciting threshold autoregression (SETAR), threshold effect, Volatility Index (VIX), nonlinear time series

JEL Classification: C22, C24, C51