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Efficient Method Of Moments Estimators For Integer Time Series Models

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  • Vance L. Martin
  • Andrew R. Tremayne
  • Robert C. Jung

Abstract

type="main" xml:id="jtsa12078-abs-0001"> The parameters of integer autoregressive models with Poisson, or negative binomial innovations can be estimated by maximum likelihood where the prediction error decomposition, together with convolution methods, is used to write down the likelihood function. When a moving average component is introduced this is not the case. To address this problem an efficient method of moment estimator is proposed where the estimated standard errors for the parameters are obtained using subsampling methods. The small sample properties of the estimator are investigated using Monte Carlo methods, while the approach is demonstrated using two well-known examples from the time series literature.

Suggested Citation

  • Vance L. Martin & Andrew R. Tremayne & Robert C. Jung, 2014. "Efficient Method Of Moments Estimators For Integer Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 491-516, November.
  • Handle: RePEc:bla:jtsera:v:35:y:2014:i:6:p:491-516
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    File URL: http://hdl.handle.net/10.1111/jtsa.12078
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    References listed on IDEAS

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    1. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 63-84, Suppl. De.
    2. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    3. Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
    4. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    5. Brendan P. M. McCabe & Gael M. Martin & David Harris, 2011. "Efficient probabilistic forecasts for counts," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 253-272, March.
    6. Feike C. Drost & Ramon van den Akker & Bas J. M. Werker, 2009. "Efficient estimation of auto-regression parameters and innovation distributions for semiparametric integer-valued AR("p") models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 467-485.
    7. Chen, Willa W. & Deo, Rohit S., 2006. "Estimation of mis-specified long memory models," Journal of Econometrics, Elsevier, vol. 134(1), pages 257-281, September.
    8. McCabe, B.P.M. & Martin, G.M., 2005. "Bayesian predictions of low count time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 315-330.
    9. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    10. Jung, Robert C. & Tremayne, A.R., 2006. "Coherent forecasting in integer time series models," International Journal of Forecasting, Elsevier, vol. 22(2), pages 223-238.
    11. Robert Jung & Gerd Ronning & A. Tremayne, 2005. "Estimation in conditional first order autoregression with discrete support," Statistical Papers, Springer, vol. 46(2), pages 195-224, April.
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    Cited by:

    1. David T. Frazier & Dan Zhu, 2017. "Derivative-Based Optimization with a Non-Smooth Simulated Criterion," Papers 1708.02365, arXiv.org.
    2. David T. Frazier & Worapree Maneesoonthorn & Gael M. Martin & Brendan P.M. McCabe, 2018. "Approximate Bayesian forecasting," Monash Econometrics and Business Statistics Working Papers 2/18, Monash University, Department of Econometrics and Business Statistics.

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