A1315
Title: Difference-based inference and estimation for long-run variance function
Authors: Kin Wai Chan - The Chinese University of Hong Kong (Hong Kong) [presenting]
Yi Ho Ngan - The Chinese University of Hong Kong (Hong Kong)
Abstract: A difference-based locally smoothed estimator is proposed for the long-run variance function of locally stationary time series in the presence of a general trend. In contrast to conventional long-run variance function estimators, the new estimator admits a closed-form expression for the mean integrated squared error, revealing that the optimal bandwidths for lag truncation and local smoothing depend on two key quantities: the dependence-to-nonstationarity ratio and the dependence-and-nonstationarity strength. Based on a normal approximation, the asymptotic distribution of the maximal deviation of the proposed estimator is derived, which serves as a unified tool for constructing simultaneous confidence bands and for testing homogeneity and parametric forms of the long-run variance function in the presence of a trend. Additionally, it is shown that local and global mean variability can be quantified by the difference between difference-based and non-difference-based estimators, and new maximum-type and integrated-type tests for mean constancy and parametric trends are developed. The importance of addressing local stationarity is justified by identifying and analyzing the anti-conservative behavior of stationary quadratic-form tests when applied to nonstationary time series.
