Seminars 2009 — Abstracts

Friday, June 19

Speaker: Jiti Gao, Adelaide

Title: Estimation in Threshold Autoregressive Models with Nonstationarity

Abstract: This paper proposes a class of new nonlinear threshold autoregressive models with both stationary and nonstationary parts. Existing literature basically focuses on testing for a unit--root structure in a threshold autoregressive model. Under the null hypothesis, the model reduces to a simple random walk. Parameter estimation then becomes standard under the null hypothesis. How to estimate parameters involved in an alternative model when the null hypothesis is not true becomes a nonstandard estimation problem. This is mainly because models under such an alternative are normally null recurrent Markov chains. This paper thus proposes to establish a parameter estimation method for such nonlinear threshold autoregressive models with null recurrent structure. Under certain assumptions, we show that the ordinary least squares (OLS) estimates of the parameters involved are asymptotically consistent. Furthermore, it can be shown that the OLS estimator of the coefficient parameter involved in the stationary part can still be asymptotically normal while the OLS estimator of the coefficient parameter involved in the nonstationary part has a nonstandard asymptotic distribution. The proposed theory and estimation method is illustrated by an example of implementation.