Testing For Threshold Nonlinearity in Short-Term Interest Rates
Concordia University and CIREQ
Address correspondence to Nikolay Gospodinov, Department of Economics, Concordia University, 1455 de Maisonneuve Blvd. West, Montréal, Québec, H3G 1M8 Canada, or e-mail: gospodin{at}alcor.concordia.ca
Received March 2, 2004; revised January 17, 2005; accepted March 2, 2005.
This article addresses some empirical problems in the term structure of interest rates using a threshold autoregressive framework with GARCH errors. This framework provides a parsimonious representation of some stylized features of interest rate data and facilitates statistical inference in the presence of high persistence and conditional heteroskedasticity. We propose a bootstrap-based LM test for linearity in the conditional mean and variance functions. The empirical results indicate a presence of threshold nonlinearities in the AR and GARCH representations of the conditional moments of short-term rate. The explicit modeling of these nonlinearities appears to improve the stability properties of the process for spot rate. The article also reports that allowing for threshold nonlinearities in conditional mean and variance leads to significant forecast improvements. The economic significance of these findings is evaluated by the term structure implications of the estimated TAR-GARCH model.
KEYWORDS: bootstrap, GARCH, persistence, threshold nonlinearity