TESTING AND MODELING MULTIVARIATE THRESHOLD MODELS

Threshold autoregressive models in which the process is piecewise line ar in the threshold space have received much attention in recent years . In this article I use predictive residuals to construct a lest stati stic for detecting threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model. The t hresholds and the model are selected jointly based on the Akaike infor mation criterion. The finite-sample performance of the proposed test i s studied by simulation. The modeling procedure is then used to study arbitrage in security markers 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 partic ular application. thresholds are determined in part by the transaction costs. I also apply the proposed procedure to U.S. monthly interest r ates and two river flow series of Iceland.