TESTING HYPOTHESES ABOUT THE NUMBER OF FACTORS IN LARGE FACTOR MODELS

• 成果类型: Article
• 署名作者: Onatski, Alexei
• 署名单位: Columbia University
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA6964
• 发表日期: 2009
• 页码: 1447-1479
• 关键词: TRACY-WIDOM LIMIT; LARGEST EIGENVALUES; UNIVERSALITY

摘要

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(h0<= h) (gamma(k) - gamma(h+1))/(gamma(h+1) - gamma(h+2)), where gamma, is the ith largest eigen-value 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, its 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.