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Estimation of mis-specified long memory models

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  • Chen, Willa W.
  • Deo, Rohit S.

Abstract

We study the asymptotic behaviour of frequency domain maximum likelihood estimators of mis-specified models of long memory Gaussian series. We show that even if the long memory structure of the time series is correctly specified, mis-specification of the short memory dynamics may result in estimators of both long- and short-memory parameters that are slower than √n consistent for the pseudo-true parameter values, which in general differ from the true values. The conditions under which this happens are provided and the asymptotic distribution of the estimators is shown to be non-Gaussian. Conditions under which estimators of the parameters of the mis-specified model have the standard √n consistency for the pseudo-true values and are asymptotically normal are also provided.
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Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:134:y:2006:i:1:p:257-281
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    References listed on IDEAS

    as
    1. R. S. Deo, 1997. "Asymptotic theory for certain regression models with long memory errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(4), pages 385-393, July.
    2. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    3. Chen, Willa W. & Deo, Rohit S., 2004. "A Generalized Portmanteau Goodness-Of-Fit Test For Time Series Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 382-416, April.
    4. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    5. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    6. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    7. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    8. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
    9. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
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    Cited by:

    1. Deo, Rohit & Hurvich, Clifford & Lu, Yi, 2006. "Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 29-58.
    2. Kanchana Nadarajah & Gael M Martin & Donald S Poskitt, 2019. "Optimal Bias Correction of the Log-periodogram Estimator of the Fractional Parameter: A Jackknife Approach," Monash Econometrics and Business Statistics Working Papers 7/19, Monash University, Department of Econometrics and Business Statistics.
    3. Martin, Gael M. & Nadarajah, K. & Poskitt, D.S., 2020. "Issues in the estimation of mis-specified models of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 215(2), pages 559-573.
    4. 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.

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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