Thursday 21 Jun 2018Bootstrap Estimation Methods for Costationarity Time Series

Alessandro Cardinali - University of Plymouth

Laver building LT6 (6th Floor) 14:30-15:30

In this presentation we illustrate a novel bootstrap 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 secondorder stationary. We first review the theory of costationarity and formalize a Generalized Method of Moments (GMM) estimator for the coefficient vectors. We repeat the GMM optimization from random starting points in order to bootstrap the solution space of (multiple) costationary coeffi- cient vectors. We then use the bootstrapped costationary combinations to create a linear system from which (costationary) factors are estimated in order to summarize representative costationary combinations.

As a first application of our approach we use this new framework to derive an efficient bootstrap estimator for the (time-varying) covariance of locally stationary time series. We show that the new covariance estimator has smaller variance than the available estimators exclusively based on the evolutionary cross-periodogram, and is therefore appealing in a large number of applications. We confirm our theoretical findings through a simulation experiment. This shows that our approach improves substantially over competitors for finite sample sizes which are of common use. We then present a new analysis of the FTSE and SP500 log return series. We also analyze DEM/USD and GBP/USD exchange rate return series and show that our new estimator compares favorably with existing approaches and is capable to highlight well known economic shocks in a clearer manner. As a second application of our approach we finally discuss bootstrap forecasting of locally stationary time series based on costationary combinations.

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