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Estimation for first-order autoregressive processes with positive or bounded innovations

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  • Davis, Richard A.
  • McCormick, William P.

Abstract

We consider estimates motivated by extreme value theory for the correlation parameter of a first-order autoregressive process whose innovation distribution F is either positive or supported on a finite interval. In the positive support case, F is assumed to be regularly varying at zero, whereas in the finite support case, F is assumed to be regularly varying at the two endpoints of the support. Examples include the exponential distribution and the uniform distribution on [-1, 1 ]. The limit distribution of the proposed estimators is derived using point process techniques. These estimators can be vastly superior to the classical least squares estimator especially when the exponent of regular variation is small.

Suggested Citation

  • Davis, Richard A. & McCormick, William P., 1989. "Estimation for first-order autoregressive processes with positive or bounded innovations," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 237-250, April.
    • Handle: RePEc:eee:spapps:v:31:y:1989:i:2:p:237-250
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    Citations

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    Cited by:

    1. Brown, Tim C. & Feigin, Paul D. & Pallant, Diana L., 1996. "Estimation for a class of positive nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 139-152, November.
    2. Preve, Daniel, 2015. "Linear programming-based estimators in nonnegative autoregression," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 225-234.
    3. Preve, Daniel & Medeiros, Marcelo C., 2011. "Linear programming-based estimators in simple linear regression," Journal of Econometrics, Elsevier, vol. 165(1), pages 128-136.
    4. Ching-Kang Ing & Chiao-Yi Yang, 2014. "Predictor Selection for Positive Autoregressive Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 243-253, March.
    5. Anders Eriksson & Daniel P. A. Preve & Jun Yu, 2019. "Forecasting Realized Volatility Using a Nonnegative Semiparametric Model," JRFM, MDPI, vol. 12(3), pages 1-23, August.
    6. J. Zhou & I. V. Basawa, 2005. "Maximum Likelihood Estimation for a First‐Order Bifurcating Autoregressive Process with Exponential Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 825-842, November.
    7. Zhang, Chenhua, 2011. "Parameter estimation for first-order bifurcating autoregressive processes with Weibull innovations," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1961-1969.
    8. Shu, Yin & Feng, Qianmei & Liu, Hao, 2019. "Using degradation-with-jump measures to estimate life characteristics of lithium-ion battery," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    9. Allen, Michael R. & Datta, Somnath, 1999. "Estimation of the index parameter for autoregressive data using the estimated innovations," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 315-324, February.
    10. Isabel Pereira & M. Antonia Amaral-Turkman, 2004. "Bayesian prediction in threshold autoregressive models with exponential white noise," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 45-64, June.
    11. Vicky Fasen & Florian Fuchs, 2013. "Spectral estimates for high-frequency sampled continuous-time autoregressive moving average processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 532-551, September.

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