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Estimation of mis-specified long memory models

By Willa Chen and Rohit Deo


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 ãn 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 ãn consistency for the pseudo-true values and are asymptotically normal are also provided.long memory, model mis-specification

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  1. (2004). A Generalized Portmanteau Goodness-of-fit Test for Time Series Models.
  2. (1984). A Pseudomaximum likelihood methods: applications to Poisson models.
  3. (1984). A Pseudomaximum likelihood methods: theory.
  4. (1993). Asymptotic properties of estimates in incorrect ARMA models for long-memory time series.
  5. (1997). Asymptotic theory for certain regression models with long memory errors.
  6. (1999). Broadband log-periodogram regression of time series with long-range dependence,
  7. (1989). Efficient parameter estimation for self-similar processes.
  8. (1978). Estimating the dimension of a model.
  9. (1953). Estimation and information in stationary time series,
  10. (1995). Gaussian semiparametric estimation of long range dependence.
  11. (1993). Indirect inference.
  12. (1973). Information theory and an extension of the maximum likelihood principle, In:
  13. (1996). Introduction to Statistical Time Series, 2’nd Ed.
  14. (1986). Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series.
  15. (1995). Log-periodogram regression of time series with long range dependence.
  16. (1982). Maximum likelihood estimation of misspecified model.
  17. (1918). On a formula for the product moment coefficient of any order of a normal frequency distribution in any number of variables.
  18. (1979). On estimation of parameters of Gaussian stationary processes.
  19. (1970). Statistical predictor identification,
  20. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. In:
  21. (1983). The estimation and application of long memory time series models.
  22. (1998). The mean squared error of Geweke and Porter-Hudak’s estimator of the memory parameter of a long-memory time series.
  23. (1996). Which moments to match?

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