A0591
Title: Bootstrap-assisted inference for weakly stationary time series
Authors: Yunyi Zhang - The Chinese University of Hong Kong, Shenzhen (China) [presenting]
Efstathios Paparoditis - University of Cyprus (Cyprus)
Dimitris Politis - University of California, San Diego (USA)
Abstract: The literature often adopts two types of stationarity assumptions in the analysis of time series, i.e., the weak stationarity, suggesting that the mean and the autocovariance function of a time series are time-invariant, and strict stationarity, indicating that the marginal distributions of the time series are time-invariant. While the strict stationarity assumption is vital from a theoretical aspect, it is hard to verify in practice. On the other hand, weak stationarity is relatively feasible, as it relies only on the second-order structures of the time series. Concerning this, statisticians may want to avoid relying on strict stationarity assumptions during statistical inference. The focus is on the analysis of quadratic forms within a weakly stationary time series. Specifically, it establishes the Gaussian approximation for quadratic forms of a short-range dependent weakly stationary time series. Building upon this result, the asymptotic distributions of the sample autocovariance, the sample autocorrelations, and the sample autoregressive coefficients are derived. Furthermore, it adopts the dependent wild bootstrap method to facilitate statistical inference. Numerical results verify the consistency of the proposed theories and methods. Strict stationarity is hard to ensure and verify for a real-life dataset. Therefore, the results should be able to assist statisticians in analyzing real-life time series.
