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Efficiency Improvements in Inference on Stationary and Nonstationary Fractional Time Series

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  • Peter M Robinson

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 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 Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2004/480.

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Date of creation: Nov 2004
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Handle: RePEc:cep:stiecm:/2004/480

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: fractional processes; efficient semiparametric estimation; adaptive estimation; nonstationary processes; series estimation; M-estimation;

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  1. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, vol. 38(3), pages 301-339, July.
  2. Marc Hallin & Abdeslam Serroukh, 1998. "Adaptive Estimation of the Lag of a Long–memory Process," Statistical Inference for Stochastic Processes, Springer, vol. 1(2), pages 111-129, May.
  3. Drost, F.C. & Klaasens, C.A.J. & Werker, B.J.M., 1994. "Adaptive Estimation in Time Series Models," Papers 9488, Tilburg - Center for Economic Research.
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Cited by:
  1. Robinson, P.M. & Iacone, F., 2005. "Cointegration in fractional systems with deterministic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 263-298.
  2. Peter M Robinson, 2006. "Conditional-Sum-of-Squares Estimation ofModels for Stationary Time Series with Long Memory," STICERD - Econometrics Paper Series /2006/505, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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