Geodesic
On unequally spaced AR(1) process
Kybernetika, Tome 39 (2003) no. 1, pp. 13-27 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Discrete autoregressive process of the first order is considered. The process is observed at unequally spaced time instants. Both least squares estimate and maximum likelihood estimate of the autocorrelation coefficient are analyzed. We show some dangers related with the estimates when the true value of the autocorrelation coefficient is small. Monte-Carlo method is used to illustrate the problems.
Discrete autoregressive process of the first order is considered. The process is observed at unequally spaced time instants. Both least squares estimate and maximum likelihood estimate of the autocorrelation coefficient are analyzed. We show some dangers related with the estimates when the true value of the autocorrelation coefficient is small. Monte-Carlo method is used to illustrate the problems.
Classification : 60G10, 62M10
Keywords: AR(1) process; unequally spaced; autocorrelation coefficient; least squares estimate; maximum likelihood estimate 
@article{KYB_2003_39_1_a1,
     author = {\v{S}indel\'a\v{r}, Jan and Kn{\'\i}\v{z}ek, Ji\v{r}{\'\i}},
     title = {On unequally spaced {AR(1)} process},
     journal = {Kybernetika},
     pages = {13--27},
     year = {2003},
     volume = {39},
     number = {1},
     mrnumber = {1980121},
     zbl = {1249.60071},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003_39_1_a1/}
}
TY  - JOUR
AU  - Šindelář, Jan
AU  - Knížek, Jiří
TI  - On unequally spaced AR(1) process
JO  - Kybernetika
PY  - 2003
SP  - 13
EP  - 27
VL  - 39
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/KYB_2003_39_1_a1/
LA  - en
ID  - KYB_2003_39_1_a1
ER  - 
%0 Journal Article
%A Šindelář, Jan
%A Knížek, Jiří
%T On unequally spaced AR(1) process
%J Kybernetika
%D 2003
%P 13-27
%V 39
%N 1
%U http://geodesic.mathdoc.fr/item/KYB_2003_39_1_a1/
%G en
%F KYB_2003_39_1_a1
Šindelář, Jan; Knížek, Jiří. On unequally spaced AR(1) process. Kybernetika, Tome 39 (2003) no. 1, pp. 13-27. http://geodesic.mathdoc.fr/item/KYB_2003_39_1_a1/

[1] Anderson T. W.: The Statistical Analysis of Time Series. Wiley, New York 1971 | MR | Zbl

[2] Baltagi B. H., Wu P. X.: Unequally spaced panel data regressions with AR(1) disturbances. Econometric Theory 15 (1999), 814–823 | DOI | Zbl

[3] Diggle P. J., Liang K. Y., Zeger S. L.: Analysis of Longitudinal Data. Oxford University Press, New York 1994 | Zbl

[4] Hauser M. A.: Maximum likelihood estimators for ARMA and ARFIMA models: a Monte Carlo study. J. Statist. Plann. Inference 80 (1999), 229–255 | DOI | MR | Zbl

[5] Jones R. H.: Longitudinal Data with Serial Correlation: A State-space Approach. Chapman & Hall, New York 1993 | MR | Zbl

[7] Jones R. H., Boadi-Boateng F.: Unequally spaced longitudinal data with AR(1) serial correlation. Biometrics 47 (1991), 161–175 | DOI

[8] Jones R. H., Vecchia A. V.: Fitting continuous ARMA models to unequally spaced spatial data. J. Amer. Statist. Assoc. 88 (1993), 947–954 | DOI | Zbl

[9] Kay S. M.: Fundamendals of Statistical Signal Prosessing: Estimation Theory. Prentice Hall, Englewood Cliffs, NJ 1993

[10] Kazakos D., Papantoni-Kazakos P.: Detection and Estimation. Computer Science Press, New York 1990

[11] Cam L. Le: Maximum likelihood: An introduction. Internat. Statist. Rev. 58 (1990), 2, 153–171 | DOI | Zbl

[12] Mckenzie D. J.: Estimation of AR(1) models with unequally spaced pseudo-panels. Econometrics J. 4 (2001), 1, 89–108 | DOI | MR

[13] Sorenson H. W.: Parameter Estimation: Principles and Problems. Marcel Dekker, New York 1980 | MR | Zbl

[14] Verbeke G., Molenberghs G.: Linear Mixed Models for Longitudinal Data. Springer Verlag, New York 2000 | MR | Zbl

[15] Zimmerman D. L., Núñez-Antón V.: Parametric modelling of growth curve data: An overview. Test, Sociedad de Estadística e Investigación Operativa 10 (2001), 1, 1–73 | DOI | MR | Zbl