Asymptotic Theory for Time Series with Changing Mean and Variance

• Activity Number: 137 - On Structural Changes
• Type: Invited
• Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Liudas Giraitis* and Violetta Dalla and Peter M Robinson
• Companies: Queen Mary University of London and National and Kapodistrian University of Athens and London School of Economics
• Keywords: Semiparametric time series model; nonparametric heteroscedasticity; nonparametric moving mean; nonparametric moving mean

Abstract

The paper develops point estimation and asymptotic theory with respect to a semiparametric model for time series with moving mean and unconditional heteroscedasticity. These two features are modelled nonparametrically, whereas autocorrelations are described by a short memory stationary parametric time series model. We consider standard implicitly-defined Whittle estimates of a general class of short memory parametric time series model. When the mean is correctly assumed to be constant, estimates that ignore the heteroscedasticity are found to be asymptotically normal but inefficient. Allowing a slowly time-varying mean we resort to trimming out of low frequencies to achieve the same outcome. Returning to finite order autoregression, nonparametric estimates of the varying mean and variance are given asymptotic justification, and forecasting formulae developed. Finite sample properties are studied by a small Monte Carlo simulation, and an empirical example is also included.