A1323
Title: Splitting high dimensional Markov chains with application to bootstrap
Authors: Patrice Bertail - Paris Nanterre University (France) [presenting]
Anna Dudek - AGH University of Krakow (Poland)
Karolina Marek-Lukasiewicz - AGH University in Krakow (Poland)
Abstract: Large-dimensional Markov chains appear in many models and many applications including analysis of electro-encephalogram data. A multidimensional approximative regenerative block bootstrap (MARBB) is introduced, a bootstrap algorithm designed for high-dimensional Markov chains. The focus is on a vector autoregressive (VAR(1)) process with a low-rank structure (but the same ideas apply for single index Markov chain models). A reduction algorithm is first used that transforms the original high-dimensional time series into a lower-dimensional Markov chain. In the cointegration (nonstationary) case, it is assumed that there are very few cointegration relationships. Once the chain is reduced, the regenerative properties of Harris recurrent Markov chains within a general state space are leveraged, using the Nummelin splitting technique to extend existing results from the one-dimensional settings to the multidimensional case. This approach enables the identification of approximate regeneration times of the lower-dimensional Markov chain, which in turn leads to the splitting of the original high-dimensional Markov chain into (almost independent) regenerative blocks. These blocks are then used to bootstrap relevant statistics based on regenerative blocks. The MARBB consistency results are obtained, and the algorithm is applied to simulated data.
