Abstract
We investigate the instability problem of the covariance structure of time series by combining the non-parametric approach based on the evolutionary spectral density theory of Priestley [Evolutionary spectra and non-stationary processes, J. R. Statist. Soc., 27 (1965), pp. 204-237; Wavelets and time-dependent spectral analysis, J. Time Ser. Anal., 17 (1996), pp. 85-103] and the parametric approach based on linear regression models of Bai and Perron [Estimating and testing linear models with multiple structural changes, Econometrica 66 (1998), pp. 47-78]. A Monte Carlo study is presented to evaluate the performance of some parametric testing and estimation procedures for models characterized by breaks in variance. We attempt to see whether these procedures perform in the same way as models characterized by mean-shifts as investigated by Bai and Perron [Multiple structural change models: a simulation analysis, in: Econometric Theory and Practice: Frontiers of Analysis and Applied Research, D. Corbea, S. Durlauf, and B.E. Hansen, eds., Cambridge University Press, 2006, pp. 212-237]. We also provide an analysis of financial data series, of which the stability of the covariance function is doubtful.