University of Liverpool
Department of Mathematical Sciences
Division of Statistics and Probability
SEMINAR
Efficiency Improvements in Inference on Stationary and Nonstationary
Fractional Time Series
P M Robinson, Department of Economics, London School of Economics
Wednesday, 17th November 2004, 2pm
The Whittaker Room (211)
Abstract:
We consider a time series model involving a fractional stochastic
component, whose integration order can lie in the stationary/invertible or
nonstationary regions and be unknown, and additive deterministic component
consisting of a generalized polynomial. The model can thus incorporate
competing descriptions of trending behaviour. The stationary input to the
stochastic component has parametric autocorrelation, but innovation with
distribution of unknown form. The model is thus semiparametric, and we
develop estimates of the parametric component which are asymptotically
normal and achieve an Mestimation efficiency bound, equal to that found in
work using an adaptive LAM/LAN approach. A major technical feature which we
treat is the effect of truncating the autoregressive representation in
order to form innovation proxies. This is relevant also when the innovation
density is parameterized, and we provide a result for that case also. Our
semiparametric estimates employ nonparametric series estimation, which
avoids some complications and conditions in kernel approaches featured in
much work on adaptive estimation of time series models; our work thus also
contributes to methods and theory for non-fractional time series models,
such as autoregressive moving averages. A Monte Carlo study of finite
sample performance of the semiparametric estimates is included. AMS 2000
subject classifications. Prima adaptive estimation, nonstationary
processes, series estimation, Mestimation.
Following the talk, tea and biscuits will be available in Room 304
ALL WELCOME
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Ingrid Harper
University of Liverpool
Department of Mathematical Sciences
Division of Statistics and Probability
Peach Street
Liverpool L69 7ZL
Tel: 0151 794 4751
Fax: 0151 794 4754
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