----------------------------------------------------------------------------- Dipartimento di Statistica e Metodi Quantitativi Via Bicocca degli Arcimboldi, 8 - 20126 Milano ----------------------------------------------------------------------------- “COSTATIONARY INFERENCE FOR LOCALLY STATIONARY TIME SERIES” Alessandro Cardinali School of Computing and Mathematics, Plymouth University University of Plymouth Lunedì 10 Luglio ore 14.00 Ed. U7, 2° piano, aula 2061 __________________________________________________________ Abstract: In this presentation we illustrate a novel inferential approach to estimate time-varying parameters of locally stationary time series. This approach is based on costationary combinations, that is, time-varying deterministic linear combinations of locally stationary time series that are second-order stationary. We first review the theory of costationarity and formalize a Generalised Method of Moments estimator for the coefficient vectors. We then use this new framework to derive an estimator for the (time-varying) covariance of locally stationary time series and we show that the new covariance estimator is more efficient than classical estimators exclusively based on the evolutionary cross-periodogram. We confirm our theoretical findings through a simulation experiment. We then present a new analysis of financial log-returns showing that our new estimator is capable to highlight well known economic shocks. As a second example of our approach we finally discuss forecasting of locally stationary time series based on costationary combinations. __________________________________________________________ Cordiali saluti Fulvia Pennoni -- Fulvia Pennoni Department of Statistics and Quantitative Methods University of Milano-Bicocca http://www.statistica.unimib.it/utenti/pennoni/