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April 2012 Factor modeling for high-dimensional time series: Inference for the number of factors
Clifford Lam, Qiwei Yao
Ann. Statist. 40(2): 694-726 (April 2012). DOI: 10.1214/12-AOS970

Abstract

This paper deals with the factor modeling for high-dimensional time series based on a dimension-reduction viewpoint. Under stationary settings, the inference is simple in the sense that both the number of factors and the factor loadings are estimated in terms of an eigenanalysis for a nonnegative definite matrix, and is therefore applicable when the dimension of time series is on the order of a few thousands. Asymptotic properties of the proposed method are investigated under two settings: (i) the sample size goes to infinity while the dimension of time series is fixed; and (ii) both the sample size and the dimension of time series go to infinity together. In particular, our estimators for zero-eigenvalues enjoy faster convergence (or slower divergence) rates, hence making the estimation for the number of factors easier. In particular, when the sample size and the dimension of time series go to infinity together, the estimators for the eigenvalues are no longer consistent. However, our estimator for the number of the factors, which is based on the ratios of the estimated eigenvalues, still works fine. Furthermore, this estimation shows the so-called “blessing of dimensionality” property in the sense that the performance of the estimation may improve when the dimension of time series increases. A two-step procedure is investigated when the factors are of different degrees of strength. Numerical illustration with both simulated and real data is also reported.

Citation

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Clifford Lam. Qiwei Yao. "Factor modeling for high-dimensional time series: Inference for the number of factors." Ann. Statist. 40 (2) 694 - 726, April 2012. https://doi.org/10.1214/12-AOS970

Information

Published: April 2012
First available in Project Euclid: 17 May 2012

zbMATH: 1273.62214
MathSciNet: MR2933663
Digital Object Identifier: 10.1214/12-AOS970

Subjects:
Primary: 62H30 , 62M10
Secondary: 60G99

Keywords: Autocovariance matrices , blessing of dimensionality , eigenanalysis , fast convergence rates , multivariate time series , ratio-based estimator , strength of factors , White noise

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 2 • April 2012
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