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Likelihood analysis of a first‐order autoregressive model with exponential innovations

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  • B. Nielsen
  • N. Shephard

Abstract

. This paper derives the exact distribution of the maximum likelihood estimator of a first‐order linear autoregression with an exponential disturbance term. We also show that, even if the process is stationary, the estimator is T‐consistent, where T is the sample size. In the unit root case, the estimator is T2‐consistent, while, in the explosive case, the estimator is ρT‐consistent. Further, the likelihood ratio test statistic for a simple hypothesis on the autoregressive parameter is asymptotically uniform for all values of the parameter.

Suggested Citation

  • B. Nielsen & N. Shephard, 2003. "Likelihood analysis of a first‐order autoregressive model with exponential innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 337-344, May.
    • Handle: RePEc:bla:jtsera:v:24:y:2003:i:3:p:337-344
    DOI: 10.1111/1467-9892.00310
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    References listed on IDEAS

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    1. Sim, C. H., 1992. "Point processes with correlated gamma interarrival times," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 135-141, September.
    2. Lai, T. L. & Wei, C. Z., 1983. "Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 1-23, March.
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    Cited by:

    1. Kleppe, Tore Selland & Skaug, Hans J., 2008. "Simulated maximum likelihood for general stochastic volatility models: a change of variable approach," MPRA Paper 12022, University Library of Munich, Germany.
    2. 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.
    3. Preve, Daniel, 2015. "Linear programming-based estimators in nonnegative autoregression," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 225-234.
    4. Preve, Daniel & Medeiros, Marcelo C., 2011. "Linear programming-based estimators in simple linear regression," Journal of Econometrics, Elsevier, vol. 165(1), pages 128-136.
    5. 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.
    6. Knight, Keith, 2003. "Asymptotic theory for M-estimators of boundaries," SFB 373 Discussion Papers 2003,37, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. Kleppe, Tore Selland & Skaug, Hans Julius, 2012. "Fitting general stochastic volatility models using Laplace accelerated sequential importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3105-3119.
    8. 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.
    9. Marek Omelka & Šárka Hudecová & Natalie Neumeyer, 2021. "Maximum pseudo‐likelihood estimation based on estimated residuals in copula semiparametric models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1433-1473, December.

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