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Keywords:
ARMA model; spectral analysis
ARMA model; spectral analysis
Summary:
The paper is devoted to the spectrum of multivariate randomly sampled autoregressive moving-average (ARMA) models. We determine precisely the spectrum numerator coefficients of the randomly sampled ARMA models. We give results when the non-zero poles of the initial ARMA model are simple. We first prove the results when the probability generating function of the random sampling law is injective, then we precise the results when it is not injective.
References:
[1] Bloomfield P.: Spectral analysis with randomly missing observations. J. Roy. Statist. Soc. B 32 (1970), 369–380 MR 0287653 | Zbl 0218.62111
[2] Brillinger D. R.: Statistical inference for irregularly observed processes. In: Proceeding of a Symposium Time Series Analysis of Irregularly Observed Data (E. Parzen, ed., Lecture Notes in Statistics 25), Springer Verlag, Berlin 1983 MR 0775893
[3] Dunsmuir W.: Estimation for stationary time series when data are irregularly spaced or missing. In: Applied Time Series II (D. F. Findley, ed.), Academic Press, New York 1981 Zbl 0482.62081
[4] Dunsmuir W.: A central limit theorem for estimation in Gaussian stationary time series observed at unequally spaced times. Stochastic Process. Appl. 14 (1983), 279–295 DOI 10.1016/0304-4149(83)90005-4 | MR 0688611 | Zbl 0502.62073
[5] Dunsmuir W.: Large sample properties of estimation in time series observed at unequally spaced times. In: Proceeding of a Symposium Time Series Analysis of Irregularly Observed Data (E. Parzen, ed., Lecture Notes in Statistics 25), Springer Verlag, Berlin 1983 MR 0775894 | Zbl 0566.62078
[6] Dunsmuir W., Robinson P. M.: Parametric estimators for stationary time series with missing observations. Adv. in Appl. Probab. 13 (1981), 126–146 DOI 10.2307/1426471 | MR 0595891 | Zbl 0461.62075
[7] Dunsmuir W., Robinson P. M.: Asymptotic theory for time series containing missing and amplitude modulated observations. Sankhyā Ser. A 43 (1981), Pt. 3, 260–281 MR 0665872 | Zbl 0531.62079
[8] Dunsmuir W., Robinson P. M.: Estimation of time series models in the presence of missing data. J. Amer. Statist. Assoc. 76 (1981), 375, 560–568 DOI 10.1080/01621459.1981.10477687 | Zbl 0471.62089
[9] Hannan E. J.: Multiple Time Series. Wiley, New York 1970 MR 0279952 | Zbl 0279.62025
[10] Kadi A.: Agrégation et échantillonnage aléatoire de séries temporelles. Thèse, Université de Paris–Sud 1994
[11] Kadi A., Oppenheim G., Viano M. C.: Random aggregation of uni and multivariate linear proceses. J. Time Ser. Anal. 15 (1994), 1, 31–43 DOI 10.1111/j.1467-9892.1994.tb00175.x | MR 1256855
[12] Kadi A., Mokkadem A.: Matrix representations of spectral coefficients of ARMA models randomly sampled. Stochastic Process. Appl. 54 (1994), 1, 121–137 DOI 10.1016/0304-4149(94)00009-3 | MR 1302698
[13] Marshall R. J.: Autocorrelation estimation of time series with randomly missing observations. Biometrika 67 (1980), 3, 567–570 DOI 10.1093/biomet/67.3.567 | MR 0601092 | Zbl 0442.62071
[14] Parzen E.: On spectral analysis with missing observations and amplitude modulation. Sankhyā, Ser. A 25 (1963), 383–392 MR 0172435 | Zbl 0136.40701
[15] Robinson P. M.: Continuous model fitting from discrete data. In: Directions in Time Series (D. R. Brillinger and G. C. Tiao, eds.), Institute of Mathematical Statistics 1980, pp. 263–278 MR 0624656
[16] Robinson P. M.: Multiple time series analysis of irregularly spaced data. In: Proceeding of a Symposium Time Series Analysis of Irregularly Observed Data (E. Parzen, ed., Lecture Notes in Statistics 25), Springer Verlag, Berlin 1983 MR 0775903 | Zbl 0556.62063
[17] Shapiro H. S., Silverman R. A.: Alias–free sampling of random noise. J. Soc. Indust. Appl. Math. 8 (1960), 2, 225–248 DOI 10.1137/0108013 | MR 0121948 | Zbl 0121.14204
[18] Toloi C. M. C., Morettin P. A.: Spectral analysis for amplitude–modulated time series. J. Time Ser. Anal. 14 (1993), 4, 409–432 DOI 10.1111/j.1467-9892.1993.tb00154.x | MR 1234583 | Zbl 0787.62097
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