RSFAS Statistics Seminar - Daning Bi and Adam Nie

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Speaker: Daning Bi and Adam Nie

Institution: RSFAS, ANU

Abstract: We study the asymptotic theory of factor models for high-dimensional time series and provide the central limit theorem (CLT) for spiked eigenvalues of high-dimensional sample auto-covariance matrices. Under a general high-dimensional setting where both dimension p and sample size T go to infinity and p/T converges to c > 0, we consider high-dimensional time series to follow a factor model where both the temporal and cross-sectional dependence are assumed to be captured by a number of factors. The limiting normal distributions for spiked eigenvalues of high-dimensional sample auto-covariance matrices are established for both cases with either fixed or diverging lags of auto-covariance. Additionally, as a statistical application of the CLT, a novel auto-covariance test is proposed based on the difference between spiked eigenvalues of sample auto-covariance matrices for two high-dimensional time series. This auto-covariance test provides statistical inferences for comparing the spectral properties of two high-dimensional time series and facilitates further statistical applications such as clusterings on multiple population high-dimensional time series. Lastly, empirical simulations, as well as analysis of worldwide mortality data, are also provided.

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