Efficiency Improvements in Inference on Stationary and Nonstationary Fractional Time Series
AbstractWe 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 generalised 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 M-estimation 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 parameterised, 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.
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Bibliographic InfoPaper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2004/480.
Date of creation: Nov 2004
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fractional processes; efficient semiparametric estimation; adaptive estimation; nonstationary processes; series estimation; M-estimation;
Find related papers by JEL classification:
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-01-02 (All new papers)
- NEP-ECM-2005-01-02 (Econometrics)
- NEP-ETS-2005-01-02 (Econometric Time Series)
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