Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

STRONG CONSISTENCY FOR AR MODEL WITH MISSING DATA

  • Published : 2004.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper is concerned with the strong consistency of the estimators of the autocovariance function and the spectral density function for the autoregressive process in the case where only an amplitude modulated process with missing data is observed. These results will give a simple and practical sufficient condition for the strong consistency of those estimators. Finally, some examples are given to illustrate the application of main result.

Keywords

References

  1. K. N. Berk, Consistent autoregressive spectral estimates., Ann. Statist. 2 (1974), no. 3, 489–502. https://doi.org/10.1214/aos/1176342709
  2. P. Bloomfield, Spectral analysis with randomly missed observations, J. R. Stat. Soc. Ser. B Stat. Methodol. 32 (1970), 369–380.
  3. R. Dahlhaus, Nonparametric spectral analysis with missing observations, Sankhya Ser. A. 49 (1987), 347–367.
  4. W. Dunsmuir and P. M. Robinson, Asymptotic theory for time series containing missing and amplitude modulated observations., Sankhya Ser. A 43 (1981a), 260–281.
  5. W. Dunsmuir and P. M. Robinson, Parametric estimators for stationary time series with missing observations., Adv. Appl. Prob. 13 (1981b), 126–146. https://doi.org/10.2307/1426471
  6. W. A. Fuller, Introduction to statistical time series, John Willy, New York (1976).
  7. H. Hall and C. C. Heyde, Martingale limit theory and its application., Academic Press (1980).
  8. S. Haykin, Nonlinear methods of spectral analysis., Springer-Verlag (1979).
  9. R. H. Jones, Spectral analysis with regularly missed observations, Ann. Math. Statist. 32 (1962), 455–461. https://doi.org/10.1214/aoms/1177704572
  10. R. E. Kromer, Asymptotic properties of the autoregressive spectral estimator., Ph. D. Dissertation, Stanford Univ. (1970).
  11. R. J. Marshall, Autocorrelation estimation of time series with randomly missing observations., Biometrika 67 (1980), no. 3, 567–570. https://doi.org/10.1093/biomet/67.3.567
  12. E. Parzen, On spectral analysis with missing observations and amplitude modulation,, Tech. Rep. 46 (1962).
  13. M. B. Priestley, Spectral analysis and time series, Academic Press (1981), 321–330.
  14. P. Revesz, The laws of large numbers, Academic Press (1968).
  15. P. A. Scheinok, Spectral analysis with randomly missed observations: the binomial case., Ann. Math. Statist. 36 (1965), 971–977. https://doi.org/10.1214/aoms/1177700069

Cited by

  1. EFFICIENT NON-PARAMETRIC ESTIMATION OF THE SPECTRAL DENSITY IN THE PRESENCE OF MISSING OBSERVATIONS vol.35, pp.5, 2014, https://doi.org/10.1111/jtsa.12072
  2. On the theory of continuous time series vol.45, pp.3, 2014, https://doi.org/10.1007/s13226-014-0064-9
  3. On Two-Stage Estimation of the Spectral Density with Assigned Risk in Presence of Missing Data pp.01439782, 2018, https://doi.org/10.1111/jtsa.12435