Covariance matrix estimation and linear process bootstrap for multivariate time series of possibly increasing dimension
By Carsten Jentsch, Dimitris Nicolas Politis. 2015
46 citations recorded by the source corpus.
Multivariate time series present many challenges, especially when they are high dimensional. The paper’s focus is twofold. First, we address the subject of consistently estimating the autocovariance sequence; this is a sequence of matrices that we conveniently stack into one huge matrix. We are then able to show consistency of an estimator based on the so-called flat-top tapers; most importantly, the consistency holds true even when the time series dimension is allowed to increase with the sample size. Secondly, we revisit the linear process bootstrap (LPB) procedure proposed by McMurry and Politis (Journal of Time Series Analysis, 2010) for univariate time series. Based on the aforementioned stacked autocovariance matrix estimator, we are able to define a version of the LPB valid for multivariate time series. Under rather general assumptions, we show that our multivariate linear process bootstrap (MLPB) has asymptotic validity for the sample mean in two important cases: (a) when the time series dimension is fixed, and (b) when it is allowed to increase with sample size. As an aside, in case (a) we show that the MLPB works also for spectral density estimators which is a novel result even in the univariate case. We conclude with a simulation study that demonstrates the superiority of the MLPB in some important cases.
Subfields: Economics and Econometrics, Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/03c04706de5f05a20563b878d4c31eaa3c4d697e
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Citations in the corpus
- Change-point detection in panel data via double CUSUM statistic (2016, background): “Some recent efforts in this direction include Jentsch and Politis (2015), who proposed the Linear Process Bootstrap for multivariate time series and established its asymptotic validity for the sample mean when n is allowed to increase with T .”
- Simultaneous multiple change-point and factor analysis for high-dimensional time series (2016, unknown): “224 M. Barigozzi et al. / Journal of Econometrics 206 (2018) 187–225 For the stationarity testing in multivariate (finite-dimensional) time series, Jentsch and Politis (2015) proposed to modify the above p as per the theory developed for the consistency of their stationary bootstrap, by (a)…”