| Summary: | 碩士 === 國立臺灣大學 === 經濟學研究所 === 105 === Model selection for the autoregressive models with exogenous inputs (ARX models) is studied in this paper. In particular, we consider the situation where the series is possibly non-stationary and a large number of predictors (even larger than the sample size) is available. Inspired by Ing and Lai (2011)’s OGA+HDIC+Trim, we propose to replace the orthogonal greedy algorithm (OGA) by the partial least squares (PLS) as forward inclusion algorithm, which we call the PLS+HDIC+Trim. The PLS+HDIC+Trim has a strong model selection ability even when the regressors are non-stationary. Therefore, this new method is still valid without any prior knowledge of the integration order or under models that are not difference-stationary. Also, we propose an order selection scheme that can select the integration order for difference- stationary models. Simulation studies also showed that the PLS+HDIC+Trim outperformed other high-dimensional methods. We apply this new method to U.S. macroeconomic data.
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