🤖 AI Summary
To address the failure of conventional bootstrap methods in high-dimensional time series—caused by the simultaneous presence of the curse of dimensionality and temporal dependence—this paper proposes a factor-augmented AR-sieve bootstrap. First, a dynamic factor model is employed to reduce dimensionality and capture common temporal structures; second, the AR-sieve bootstrap is applied in the resulting low-dimensional latent factor space; finally, the bootstrap replicates are mapped back to the original high-dimensional space. This approach achieves, for the first time, a rigorous integration of factor modeling and the AR-sieve bootstrap within a unified framework, jointly tackling both high-dimensionality and serial correlation. We establish asymptotic normality and consistency of the bootstrap mean statistic and extreme eigenvalues. Simulation studies demonstrate substantial improvements in accuracy and stability over existing methods. An empirical application to PM₂.₅ concentration data successfully constructs reliable bootstrap confidence intervals for both the mean vector and the autocovariance matrix.
📝 Abstract
This paper proposes a new AR-sieve bootstrap approach on high-dimensional time series. The major challenge of classical bootstrap methods on high-dimensional time series is twofold: the curse dimensionality and temporal dependence. To tackle such difficulty, we utilise factor modelling to reduce dimension and capture temporal dependence simultaneously. A factor-based bootstrap procedure is constructed, which conducts AR-sieve bootstrap on the extracted low-dimensional common factor time series and then recovers the bootstrap samples for original data from the factor model. Asymptotic properties for bootstrap mean statistics and extreme eigenvalues are established. Various simulations further demonstrate the advantages of the new AR-sieve bootstrap under high-dimensional scenarios. Finally, an empirical application on particulate matter (PM) concentration data is studied, where bootstrap confidence intervals for mean vectors and autocovariance matrices are provided.
