Testing Hypotheses About the Number of Factors in Large Factor Models
针对具有广义动态因子结构的高维时间序列，提出一种检验因子数量的方法，统计量基于谱密度矩阵特征值，渐近分布服从Tracy-Widom分布，并应用于宏观经济和股票超额收益数据。
In this paper we study high-dimensional time series that have the generalized dynamic factor structure. We develop a test of the null of k 0 factors against the alternative that the number of factors is larger than k 0 but no larger than k 1 >k 0 . Our test statistic equals max k 0 >k⩽k 1 (Gamma k - Gamma k+1 )(Gamma k+1 - Gamma k+2 ), where Gamma i is the ith largest eigenvalue of the smoothed periodogram estimate of the spectral density matrix of data at a prespecified frequency. We describe the asymptotic distribution of the statistic, as the dimensionality and the number of observations rise, as a function of the Tracy-Widom distribution and tabulate the critical values of the test. As an application, we test different hypotheses about the number of dynamic factors in macroeconomic time series and about the number of dynamic factors driving excess stock returns. Copyright 2009 The Econometric Society.