不穩定時間序列的高維度模型選擇

Abstract

本篇文章旨在研究如何在有外生輸入的自我迴歸模型下做模型選擇。我們特別考慮在目標時間序列可能為非穩定以及可用以預測的變數數目龐大的情形。受到Ing and Lai (2011)的OGA+HDIC+Trim的啟發，我們建議用偏最小平方法（Partial Least Squares）取代正交貪婪演算法（Orthogonal Greedy Algorithm）作為向前包含變數演算法，我們稱其為PLS+HDIC+Trim。即使在迴歸因子有可能為非穩定的情形下，PLS+HDIC+Trim仍具有相當強的模型選擇能力。因此，即使我們不知道非穩定時間序列的差分次數或是有興趣的序列不是差分穩定，PLS+HDIC+Trim能仍發揮用處。我們亦提出了一個方法來選擇差分穩定模型裡的差分次數。模擬結果顯示PLS+HDIC+Trim的表現較其他高維度方法佳。我們將此方法套用至美國總體經濟資料。

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.