B1610
Title: Multivariate multiscale model for locally stationary processes
Authors: Mathieu Sauvenier - Universite Catholique de Louvain (Belgium) [presenting]
Abstract: The prevalent models for analyzing multivariate zero mean time series typically hinge on the assumption of covariance stationarity, signifying that the second-order structure of the vector time series remains constant over time. This assumption greatly facilitates the mathematical analysis of covariance estimators. Nevertheless, many time series in applied sciences do not adhere to covariance stationarity and instead exhibit a time-varying second-order structure, where variance and covariance evolve over time. The paper's focal point is a model of locally stationary wavelet processes. Time series is conceptualized as a linear combination of certain easily tractable functions, wavelets, and random increments. These types of models have been previously explored for univariate non-stationary time series. They enable the modelling and estimation of the time-varying autocovariance. The purpose is to present a multivariate multiscale model for locally stationary processes. The model allows correlation between increments across different time series and scales, a novel achievement in the field. Identification and estimation theories are obtained via the new concept of cross-correlation wavelet functions to measure redundancy levels among sets of non-decimated discrete wavelet functions. Simulations and an econometric application demonstrate the practical utility of the method.
