Testing and Modeling Multivariate Threshold Models

Abstract

Threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years. In this article I use predictive residuals to construct a test statistic for detecting threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model. The thresholds and the model are selected jointly based on the Akaike information criterion. The finite-sample performance of the proposed test is studied by simulation. The modeling procedure is then used to study arbitrage in security markets and results in a threshold cointegration between logarithms of future contracts and spot prices of a security after adjusting for the cost of carrying the contracts. In this particular application, thresholds are determined in part by the transaction costs. I also apply the proposed procedure to U.S. monthly interest rates and two river flow series of Iceland.