Title（标题）：Uniform Inference with Stationary or Nearly Integrated Regressors Using the Restricted Likelihood

Speaker（汇报人）：Professor Yanping Yi (Shanghai University of Finance and Economics）

Time（功夫）：2012-12-04(星期二) 10:00-12:00

Place（地址）：拉斯维加斯9888新楼214室

Abstract（提要）：In this paper we consider inference using restricted likelihood for predictive regression models with unknown intercepts. The nuisance intercept parameter is the major source of culties with inference when the predictor series fXtg are highly persistent [Chen and Deo (2009)]. Restricted likelihood is free of the nuisance intercept parameter and possesses small curvature, but restricted maximum likelihood (REML) estimator of this model is generally infeasible for high dimensional case and has no closed form. The weighted least squares approximate restricted likelihood estimator introduced by [Chen and Deo (2010)] for vector autoregressive processes can be applied to our model. This estimator inherits the nice property of REML estimator, and is easier to compute. We have investigated the cases where fXtg is stationary, has moderate deviations from unity root and has local to unity root. The quasi-restricted likelihood ratio based on weighted least squares estimator (under the null) has been shown to have standard ?2 limiting distribution if the autoregressive root of fXtg is strictly less than unity or moderate deviations from unity. In the presence of nearly integrated regressor, the quasi-restricted likelihood ratio converges to a distribution a bit away from ?2 due to its nonstandard nature. However, simulation shows this nonstandard limiting distribution is very close to ?2. Therefore, by using a sup-bound critical value, quasi restricted likelihood ratio test ( RLRT) has asymptotically the correct size and very good power, uniformly. Monte Carlo studies show it has uniformly higher power than [ Jansson and Moreira, Econometrica 2006].