Problem
Research questions and friction points this paper is trying to address.
high-dimensional time series
mean testing
latent dynamic factors
strong serial dependence
factor-adjusted tests
Factor-Adjusted Location Tests for High-Dimensional Time Series
🤖 AI Summary
This study addresses the challenges of mean testing for high-dimensional time series driven by strong common factors, where conventional tests suffer from poor size control and low power. The authors propose three classes of factor-adjusted mean tests that estimate the dynamic factor loading space and project the data onto its orthogonal complement, effectively accommodating sparse, dense, and unknown sparsity structures. Under strong factor assumptions, they develop a quadratic-form test applicable when the dimension satisfies $p = o(n^2)$, establish the Gumbel limiting distribution for the maximum-type statistic and the normal limit for the quadratic-form statistic, and prove their asymptotic independence. They further validate the efficacy of the Cauchy combination test. Simulations and empirical analyses demonstrate that the proposed methods achieve accurate size control and superior power in the presence of strong cross-sectional dependence.
📝 Abstract
We study high-dimensional one-sample mean testing for time series with strong common serial dependence driven by latent dynamic factors. After estimating the dynamic factor loading space from lagged autocovariance, we project the data onto its orthogonal complement and construct three factor-adjusted tests: a max test for sparse alternatives, a quadratic test for dense alternatives, and a Cauchy combination test for unknown sparsity. The idiosyncratic component is allowed to be non-Gaussian sub-Gaussian vector white noise. We establish the Gumbel limit of the max statistic, the normal limit and local power function of the quadratic statistic, their asymptotic independence, and the validity of the Cauchy combination. In the strong-factor case, the refined projection expansion shows that the quadratic statistic remains valid for dimensions as large as $p=o(n^2)$. A random-loading residual bootstrap is developed for finite-sample calibration. Simulation studies and a real data application demonstrate reliable size control and competitive power for high-dimensional observations with strong dependence.
Innovation
Methods, ideas, or system contributions that make the work stand out.
factor-adjusted testing
high-dimensional time series
dynamic factor model
Cauchy combination test
random-loading residual bootstrap
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