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STRONG CONSISTENCY FOR AR MODEL WITH MISSING DATA
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 Title & Authors
STRONG CONSISTENCY FOR AR MODEL WITH MISSING DATA
Lee, Myung-Sook;
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 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
strong consistency;Stochastic process;stationary autoregressive process;
 Language
English
 Cited by
1.
EFFICIENT NON-PARAMETRIC ESTIMATION OF THE SPECTRAL DENSITY IN THE PRESENCE OF MISSING OBSERVATIONS, Journal of Time Series Analysis, 2014, 35, 5, 407  crossref(new windwow)
2.
On the theory of continuous time series, Indian Journal of Pure and Applied Mathematics, 2014, 45, 3, 297  crossref(new windwow)
 References
1.
K. N. Berk, Consistent autoregressive spectral estimates., Ann. Statist. 2 (1974), no. 3, 489–502. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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. crossref(new window)