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The estimation of a nonlinear moving average model

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  • Robinson, P. M.

Abstract

We consider discrete-parameter stochastic processes that are the output of a nonlinear filter driven by white noise. For a simple model, we derive estimates of the unknown coefficients in the transfer function and the noise variance, and investigate their asymptotic properties. We prove some lemmas that can also be used to obtain rates of convergence in the weak and strong laws of large numbers, and central limit theorems, for estimates of more general nonlinear models.

Suggested Citation

  • Robinson, P. M., 1977. "The estimation of a nonlinear moving average model," Stochastic Processes and their Applications, Elsevier, vol. 5(1), pages 81-90, February.
    • Handle: RePEc:eee:spapps:v:5:y:1977:i:1:p:81-90
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    Cited by:

    1. Artem Prokhorov, 2008. "Nonlinear dynamics and chaos theory in economics: a historical perspective (in Russian)," Quantile, Quantile, issue 4, pages 79-92, March.
    2. 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.
    3. Zaffaroni, Paolo & d'Italia, Banca, 2003. "Gaussian inference on certain long-range dependent volatility models," Journal of Econometrics, Elsevier, vol. 115(2), pages 199-258, August.
    4. Ren, Fei & Tian, Chenlu & Zhang, Guiqing & Li, Chengdong & Zhai, Yuan, 2022. "A hybrid method for power demand prediction of electric vehicles based on SARIMA and deep learning with integration of periodic features," Energy, Elsevier, vol. 250(C).
    5. Deepanshu Sharma & Kritika Phulli, 2020. "Forecasting and Analyzing the Military Expenditure of India Using Box-Jenkins ARIMA Model," Papers 2011.06060, arXiv.org.
    6. Korkie, Bob & Sivakumar, Ranjini & Turtle, Harry, 2002. "The dual contributions of information instruments in return models: magnitude and direction predictability," Journal of Empirical Finance, Elsevier, vol. 9(5), pages 511-523, December.
    7. Ventosa-Santaulària, Daniel & Mendoza V., Alfonso, 2005. "Non Linear Moving-Average Conditional Heteroskedasticity," MPRA Paper 58769, University Library of Munich, Germany.
    8. Daniel Ventosa-Santaulària & Alfonso Mendoza Velázquez & Manuel Gómez-Zaldívar, 2008. "Varianza condicional de medias móviles no-lineales," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 29-48, November.

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