Threshold spatial autoregressive model



主講人:李鯤鵬  首都經濟貿易大學教授




地點:騰訊會議 382 378 550






內容介紹:This paper considers the estimation and inferential issues of threshold spatial  autoregressive model, which is a hybrid of threshold model and spatial  autoregressive model. We consider using the quasi maximum likelihood (QML)  method to estimate the model. We prove the tightness and the H\'{a}jek-R\'{e}nyi  type inequality for a quadratic form, and establish a full inferential theory of  the QML estimator under the setup that the threshold effect shrinks to zero  along with an increasing sample size. Our analysis indicates that the limiting  distribution of the QML estimator for the threshold value is pivotal up to a  scale parameter which involves the skewness and kurtosis of the errors due to  the misspecification on the distribution of errors. The QML estimators for the  other parameters achieve the oracle property, that is, they have the same  limiting distributions as the infeasible QML estimators, which are obtained  supposing that the threshold value is observed a priori. We also consider the  hypothesis testing on the presence of threshold effect. Three super-type  statistics are proposed to perform this testing. Their asymptotic behaviors are  studied under the Pitman local alternatives. A bootstrap procedure is proposed  to obtain the asymptotically correct critical value. We also consider the  hypothesis testing on the threshold value equal to some prespecified one. We run  Monte carlo simulations to investigate the finite sample performance of the QML  estimators and find that the QML estimators have good performance.