“Plug-in” Statistical Forecasting of Vector Autoregressive Time Series with Missing Values
DOI:
https://doi.org/10.17713/ajs.v34i2.409Abstract
The problems of statistical forecasting of vector autoregressive time series with missing values are considered. The maximum likelihood forecast is constructed and its mean square risk is evaluated for the case of known parameters. The “plug-in” forecast and statistical estimators are constructed for unknown parameters. Asymptotic properties of constructed estimators are analyzed. Results of numerical experiments are presented.
References
T.W. Anderson. The Statistical Analysis of Time Series. Wiley, New York, 1st edition, 1971.
O.E. Barndorff-Nielsen and D.R. Cox. Asymptotic Techniques for Use in Statistics. Chapman and Hall, London, 1st edition, 1989.
J. Beran, R.J. Bhansali, and D. Ocker. On unified model selection for stationary and nonstationary short- and long-memory autoregressive processes. Biometrica, 85(4):
–934, 1998.
W.H. Greene. Econometric Analysis. Macmillan, New York, 1st edition, 2000.
R.H. Jones. Maximum likelihood fitting of arma models to time series with missing observations. Technometrics, 22(3):389–395, 1980.
Yu.S. Kharin2 and A.S. Huryn. Statistical analysis and forecasting of autoregressive time series under missing values. Bulletin of the International Statistic Institute, (1):612–613, 2003.
R. Little and D. Rubin. Statistical Analysis with Missing Data. Wiley, New York, 1st edition, 1987.
M. Maejima. A non-uniform estimate in the central limit theorem for m-dependent random variables. KEIO Engineering Reports, 31(2):15–20, 1978.
S.G. Pantula and D. Shin. Testing for a unit root in autoregressive processes with systematic but incomplete sampling. Stat. & Prob. Letters, 18:183–190, 1993.
J.L. Shafer. Analysis of Incomplete Data. Chapman and Hall, London, 1st edition, 1997.
V.V. Shergin. Estimate of the error term in the central limit theorem for m-dependent random variables. Lietuvos Matematikos Rinkinys, 16(4):245–250, 1976.
A.N. Shiryaev. Probability. Springer-Verlag, New York, 1st edition, 1995.
N. Stockinger and R. Dutter. Robust time series snalysis: A survey. Kybernetika, 23: 3–90, 1987.
Downloads
Published
Issue
Section
License
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.
How to Cite
