대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제47권5호
  • /
  • Pages.889-905
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  • 2010
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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CONSISTENT AND ASYMPTOTICALLY NORMAL ESTIMATORS FOR PERIODIC BILINEAR MODELS

  • 투고 : 2008.04.15
  • 심사 : 2010.03.17
  • 발행 : 2010.09.30
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초록

In this paper, a distribution free approach to the parameter estimation of a simple bilinear model with periodic coefficients is presented. The proposed method relies on minimum distance estimator based on the autocovariances of the squared process. Consistency and asymptotic normality of the estimator, as well as hypotheses testing, are derived. Numerical experiments on simulated data sets are presented to highlight the theoretical results.

키워드

참고문헌

  1. A. Bibi, On the covariance structure of time varying bilinear models, Stochastic Anal. Appl. 21 (2003), no. 1, 25-60. https://doi.org/10.1081/SAP-120017531
  2. A. Bibi and A. Aknouche, Yule-Walker type estimators in periodic bilinear models: strong consistency and asymptotic normality, Stat. Methods Appl. 19 (2010), 1-30. https://doi.org/10.1007/s10260-008-0110-z
  3. A. Bibi and A. Gautier, Proprietes dans $L^2$ et estimation des processus purement bilineaires et strictement superdiagonaux a coefficients periodiques, Canad. J. Statist. 34 (2006), no. 1, 131-148. https://doi.org/10.1002/cjs.5550340110
  4. A. Bibi and A. J. Oyet, Estimation of some bilinear time series models with time varying coefficients, Stochastic Anal. Appl. 22 (2004), no. 2, 355-376. https://doi.org/10.1081/SAP-120028595
  5. P. J. Brockwell and R. A. Davis, Introduction to Time Series and Forecasting, Springer-Verlag, New York, 1996.
  6. C. Francq, ARMA models with bilinear innovations, Comm. Statist. Stochastic Models 15 (1999), no. 1, 29-52. https://doi.org/10.1080/15326349908807524
  7. A. Gautier, Asymptotic inefficiency of mean-correction on parameter estimation for a periodic first-order autoregressive model, Comm. Statist. Theory Methods 35 (2006), no. 10-12, 2083-2106. https://doi.org/10.1080/03610920600761873
  8. A. Hall, Generalized Method of Moments, Oxford University Press, Oxford, 2005.
  9. W. K. Newey and D. McFadden, Large sample estimation and hypothesis testing, Handbook of econometrics, Vol. IV, 2111-2245, Handbooks in Econom., 2, North-Holland, Amsterdam, 1994.

피인용 문헌

  1. On periodic time-varying bilinear processes: structure and asymptotic inference vol.25, pp.3, 2016, https://doi.org/10.1007/s10260-015-0344-5
  2. Minimum distance estimation of Markov-switching bilinear processes vol.50, pp.6, 2016, https://doi.org/10.1080/02331888.2016.1229783