Simultaneous statistical inference for second order parameters of time series under weak conditions
Yunyi Zhang, Efstathios Paparoditis, Dimitris N. Politis
The Annals of Statistics · 2024 · Volume 52 · Issue 5
Abstract
Strict stationarity is an assumption commonly used in time-series analysis in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak stationarity, this paper derives the asymptotic distribution of the maximum of sample autocovariances and sample autocorrelations under weak conditions by using Gaussian approximation techniques. The asymptotic theory for parameter estimators obtained by fitting a (linear) autoregressive model to a general weakly stationary time series is revisited and a Gaussian approximation theorem for the maximum of the estimators of the autoregressive coefficients is derived. To perform statistical inference for the aforementioned second-order parameters of interest, a bootstrap algorithm, the so-called second-order wild bootstrap is applied. Consistency of the bootstrap procedure is proven without imposing strict stationary conditions or structural process assumptions, like linearity. The good finite sample performance of the second-order wild bootstrap is demonstrated by means of simulations.
Keywords
62G09, 62G20, 62M10, autoregressive model, second-order statistics, time series, weak stationarity, wild bootstrap
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