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Asymptotic Inference For Nonstationary Fractionally Integrated Autoregressive Moving-Average Models

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  • 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.

Suggested Citation

  • Ling, Shiqing & Li, W.K., 2001. "Asymptotic Inference For Nonstationary Fractionally Integrated Autoregressive Moving-Average Models," Econometric Theory, Cambridge University Press, vol. 17(4), pages 738-764, August.
    • Handle: RePEc:cup:etheor:v:17:y:2001:i:04:p:738-764_17
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    Cited by:

    1. Morten Orregaard Nielsen, 2004. "Efficient inference in multivariate fractionally integrated time series models," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 63-97, June.
    2. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    3. Johansen, Søren & Nielsen, Morten Ørregaard, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Journal of Econometrics, Elsevier, vol. 158(1), pages 51-66, September.
    4. Jakob Roland Munch & Michael Svarer, "undated". "Mortality and Socio-economic Differences in a Competing Risks Model," Economics Working Papers 2001-1, Department of Economics and Business Economics, Aarhus University.
    5. Daiqing Xi & Tianxiao Pang, 2021. "Estimating multiple breaks in mean sequentially with fractionally integrated errors," Statistical Papers, Springer, vol. 62(1), pages 451-494, February.
    6. Luis A. Gil‐Alana, 2004. "A joint test of fractional integration and structural breaks at a known period of time," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 691-700, September.

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