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Truncated sum of squares estimation of fractional time series models with deterministic trends

Author

Listed:
  • Javier Hualde

    () (Universidad Publica de Navarra)

  • Morten Ørregaard Nielsen

    () (Queen's University and CREATES)

Abstract

We consider truncated (or conditional) sum of squares estimation of a parametric model composed of a fractional time series and an additive generalized polynomial trend. Both the memory parameter, which characterizes the behaviour of the stochastic component of the model, and the exponent parameter, which drives the shape of the deterministic component, are considered not only unknown real numbers, but also lying in arbitrarily large (but finite) intervals. Thus, our model captures different forms of nonstationarity and noninvertibility. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to non-uniform convergence of the objective function over a large admissible parameter space, but, in addition, our framework is substantially more involved due to the competition between stochastic and deterministic components. We establish consistency and asymptotic normality under quite general circumstances, finding that results differ crucially depending on the relative strength of the deterministic and stochastic components.

Suggested Citation

  • Javier Hualde & Morten Ørregaard Nielsen, 2017. "Truncated sum of squares estimation of fractional time series models with deterministic trends," Working Papers 1376, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:1376
    as

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    File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1376.pdf
    File Function: First version 2017
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    References listed on IDEAS

    as
    1. Søren Johansen & Morten Ørregaard Nielsen, 2012. "Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model," Econometrica, Econometric Society, vol. 80(6), pages 2667-2732, November.
    2. Robinson, P.M. & Iacone, F., 2005. "Cointegration in fractional systems with deterministic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 263-298.
    3. P. M. Robinson & J. Hualde, 2003. "Cointegration in Fractional Systems with Unknown Integration Orders," Econometrica, Econometric Society, vol. 71(6), pages 1727-1766, November.
    4. 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.
    5. Hualde, Javier & Robinson, Peter M., 2003. "Cointegration in fractional systems with unkown integration orders," LSE Research Online Documents on Economics 58050, London School of Economics and Political Science, LSE Library.
    6. Javier Hualde & Morten Ørregaard Nielsen, 2017. "Truncated sum of squares estimation of fractional time series models with deterministic trends," Working Papers 1376, Queen's University, Department of Economics.
    7. Javier Hualde & Peter M Robinson, 2003. "Cointegration in Fractional Systems with Unkown Integration Orders," STICERD - Econometrics Paper Series 449, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    8. Yuzo Hosoya, 2005. "Fractional Invariance Principle," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 463-486, May.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Javier Hualde & Morten Ørregaard Nielsen, 2017. "Truncated sum of squares estimation of fractional time series models with deterministic trends," Working Papers 1376, Queen's University, Department of Economics.

    More about this item

    Keywords

    Asymptotic normality; consistency; deterministic trend; fractional process; generalized polynomial trend; noninvertibility; nonstationarity; truncated sum of squares estimation;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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