Summary
An estimator of the set of parameters of an autoregressive moving average model is obtained by applying the method of least squares to the log smoothed periodogram. It is shown to be asymptotically efficient and normally distributed under the normality and the circular condition of the generating process. A computational procedure is constructed by the Newton-Raphson method. Several computer simulation results are given to demonstrate the usefulness of the present procedure.
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References
Anderson, T. W. (1977). Estimation for autoregressive moving average models in the time and frequency domains,Ann. Statist.,5, 842–865.
Bloomfield, P. (1973). An exponential model for the spectrum of a scalar time series,Biometrika,60, 217–226.
Cleveland, W. S. (1972_. The inverse autocorrelations of a time series and their applications,Technometrics,14, 277–298.
Clevenson, M. L. (1970). Asymptotically efficient estimates of the parameters of a moving average time series, Ph.D. Dissertation, Department of Statistics, Stanford University.
Davis, H. T. and Jones, R. H. (1968). Estimation of the innovation variance of a stationary time series,J. Amer. Statist. Ass.,63, 141–149.
Durbin, J. (1960). The fitting of time-series models,Rev. Inst. Internat. Statist.,28, 233–244.
Hannan, E. J. (1969). The estimation of mixed moving average autoregressive systems,Biometrika,56, 579–593.
Hannan, E. J. and Nicholls, D. F. (1977). The estimation of the prediction error variance,J. Amer. Statist. Ass.,72, 834–840.
McClave, J. T. (1974). A comparison of moving average estimation procedures,Commun. Statist.,3, 865–883.
Singleton, R. C. (1969). An algorithm for computing the mixed radix fast Fourier transform,IEEE Trans. Audio and Electro., AU-17, 93–103.
Wahba, G. (1980). Automatic smoothing of the log periodogram,J. Amer. Statist. Ass.,75, 122–132.
Walker, A. M. (1962). Large-sample estimation of parametes for autoregressive processes with moving-average residuals,Biometrika,49, 117–131.
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Nakano, J. Parameter estimation of an autoregressive moving average model. Ann Inst Stat Math 34, 83–90 (1982). https://doi.org/10.1007/BF02481009
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DOI: https://doi.org/10.1007/BF02481009