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Asymptotic Inference For Nonstationary Fractionally Integrated Autoregressive Moving-Average Models

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Author Info

  • Ling, Shiqing
  • Li, W.K.

Abstract

This paper considers nonstationary fractional autoregressive integrated moving-average (p,d,q) models with the fractionally differencing parameter d ( 1/2,1/2) and the autoregression function with roots on or outside the unit circle. Asymptotic inference is based on the conditional sum of squares (CSS) estimation. Under some suitable conditions, it is shown that CSS estimators exist and are consistent. The asymptotic distributions of CSS estimators are expressed as functions of stochastic integrals of usual Brownian motions. Unlike results available in the literature, the limiting distributions of various unit roots are independent of the parameter d over the entire range d ( 1/2,1/2). This allows the unit roots and d to be estimated and tested separately without loss of efficiency. Our results are quite different from the current asymptotic theories on nonstationary long memory time series. The finite sample properties are examined for two special cases through simulations.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 17 (2001)
Issue (Month): 04 (August)
Pages: 738-764

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Handle: RePEc:cup:etheor:v:17:y:2001:i:04:p:738-764_17

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Cited by:
  1. Søren Johansen & Morten Ørregaard Nielsen, 2007. "Likelihood Inference for a Nonstationary Fractional Autoregressive Model," Discussion Papers 07-27, University of Copenhagen. Department of Economics.
  2. Morten Oerregaard Nielsen, . "Efficient Inference in Multivariate Fractionally Integrated Time Series Models," Economics Working Papers 2002-6, School of Economics and Management, University of Aarhus.
  3. Jakob Roland Munch & Michael Svarer, . "Mortality and Socio-economic Differences in a Competing Risks Model," Economics Working Papers 2001-1, School of Economics and Management, University of Aarhus.

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