Using Extraneous Information and GMM to Estimate Threshold Parameters in TAR Models

A prominent class of nonlinear time series models are threshold autoregressive models. Recently work by Kapetanios (2000) has shown in a Monte Carlo setting that the superconsistency property of the threshold parameter estimates does not translate to superior performance in small samples. Another issue concerning inference for the threshold parameters relates to estimation of their standard errors. As the asymptotic distribution of the threshold parameters is neither normal nor nuisance parameter free, an outstanding issue is how to obtain standard errors and confidence intervals for them. This paper aims to address these issues. In particular, we suggest that using extraneous information on the location of the threshold parameters may lead to better estimates. The extraneous information comes in the form of moment conditions that relate residuals of standard threshold models to shocks driving other variables. Additionally the paper considers the problem of estimating standard errors and confidence intervals for threshold parameter estimates. We suggest use of the bootstrap for this problem.