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Gaussian Maximum Likelihood Estimation For ARMA Models. I. Time Series

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  • Qiwei Yao
  • Peter J. Brockwell

Abstract

We provide a direct proof for consistency and asymptotic normality of Gaussian maximum likelihood estimators for causal and invertible autoregressive moving-average (ARMA) time series models, which were initially established by Hannan [Journal of Applied Probability (1973) vol. 10, pp. 130-145] via the asymptotic properties of a Whittle's estimator. This also paves the way to establish similar results for spatial processes presented in the follow-up article by Yao and Brockwell [Bernoulli (2006) in press]. Copyright 2006 The Authors Journal compilation 2006 Blackwell Publishing Ltd.

Suggested Citation

  • Qiwei Yao & Peter J. Brockwell, 2006. "Gaussian Maximum Likelihood Estimation For ARMA Models. I. Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 857-875, November.
  • Handle: RePEc:bla:jtsera:v:27:y:2006:i:6:p:857-875
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    Citations

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    Cited by:

    1. Søren Johansen & Marco Riani & Anthony C. Atkinson, 2012. "The Selection of ARIMA Models with or without Regressors," Discussion Papers 12-17, University of Copenhagen. Department of Economics.
    2. Zheng, Tingguo & Xiao, Han & Chen, Rong, 2015. "Generalized ARMA models with martingale difference errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 492-506.
    3. Moon, Seongman & Velasco, Carlos, 2013. "Tests for m-dependence based on sample splitting methods," Journal of Econometrics, Elsevier, vol. 173(2), pages 143-159.
    4. repec:eee:jmvana:v:158:y:2017:i:c:p:31-46 is not listed on IDEAS
    5. Robinson, P.M., 2011. "Asymptotic theory for nonparametric regression with spatial data," Journal of Econometrics, Elsevier, vol. 165(1), pages 5-19.
    6. Abdelouahab Bibi & Karima Kimouche, 2014. "On stationarity and second-order properties of bilinear random fields," Statistical Inference for Stochastic Processes, Springer, vol. 17(3), pages 221-244, October.
    7. repec:esx:essedp:767 is not listed on IDEAS
    8. Hindrayanto, Irma & Koopman, Siem Jan & Ooms, Marius, 2010. "Exact maximum likelihood estimation for non-stationary periodic time series models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2641-2654, November.
    9. Ke Zhu & Shiqing Ling, 2015. "LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 784-794, June.
    10. Hernández Juan R., 2016. "Unit Root Testing in ARMA Models: A Likelihood Ratio Approach," Working Papers 2016-03, Banco de México.
    11. Dimitriou-Fakalou, Chrysoula, 2009. "Modified Gaussian likelihood estimators for ARMA models on," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4149-4175, December.
    12. Peter M Robinson, 2011. "Inference on Power Law Spatial Trends (Running Title: Power Law Trends)," STICERD - Econometrics Paper Series 556, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. Robinson, Peter M., 2011. "Inference on power law spatial trends (Running Title: Power Law Trends)," LSE Research Online Documents on Economics 58100, London School of Economics and Political Science, LSE Library.
    14. Rosa Espejo & Nikolai Leonenko & Andriy Olenko & María Ruiz-Medina, 2015. "On a class of minimum contrast estimators for Gegenbauer random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 657-680, December.
    15. repec:bla:jorssb:v:79:y:2017:i:2:p:507-524 is not listed on IDEAS
    16. repec:bla:scjsta:v:44:y:2017:i:3:p:617-635 is not listed on IDEAS

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