AR-sieve Bootstrap for High-dimensional Time Series

Bi, Daning; Shang, Han Lin; Yang, Yanrong; Zhu, Huanjun

doi:10.2139/ssrn.3975385

Cited by 1 publication

(1 citation statement)

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“…Therefore, bootstrap methods for time series such as the sieve bootstrap can be conducted on the estimated factors for estimating v (m) i,τ and θ (m) i,τ . Next, we will apply the AR-sieve bootstrap method in [6] to get a bootstrap estimation for the unknown parameters. In specific, an AR(p) model can be fitted for each estimated factor f (m) i and the residuals can be taken as…”

Section: And σmentioning

confidence: 99%

Spiked eigenvalues of high-dimensional sample autocovariance matrices: CLT and applications

Bi¹,

Han²,

Nie³

et al. 2022

Preprint

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High-dimensional autocovariance matrices play an important role in dimension reduction for high-dimensional time series. In this article, we establish the central limit theorem (CLT) for spiked eigenvalues of high-dimensional sample autocovariance matrices, which are developed under general conditions. The spiked eigenvalues are allowed to go to infinity in a flexible way without restrictions in divergence order.Moreover, the number of spiked eigenvalues and the time lag of the autocovariance matrix under this study could be either fixed or tending to infinity when the dimension p and the time length T go to infinity together. As a further statistical application, a novel autocovariance test is proposed to detect the equivalence of spiked eigenvalues for two high-dimensional time series. Various simulation studies are illustrated to justify the theoretical findings. Furthermore, a hierarchical clustering approach based on the autocovariance test is constructed and applied to clustering mortality data from multiple countries.

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Section: And σmentioning

confidence: 99%