Statistical Forecasting of Autoregressive Time Series under Missing Values: Optimality and Robustness

We consider the problem of robustness in statistical forecasting of autoregressive time series where distortions are generated by missing values [1–3]. The main results of this paper are:
● the new statistical estimators of the parameters of vector autoregressive time series under missing values are constructed and their asymptotic properties (consistency and asymptotic normality) are proved.
● the optimal in the maximum likelihood sense forecasting statistics are constructed for the vector autoregressive time series under missing values and known parameters and their matrix risks of forecasting are evaluated.
● the “plug-in” forecasting statistics for the vector autoregressive time series under missing values and unknown coefficients are constructed and the asymptotic expansions of their matrix risks of forecasting are found.

References
1. Little, R.J.A. Statistical Analysis with Missing Data / R.J.A. Little, D.B. Rubin. — New York: John Wiley & Sons, 1987.
2. Kharin, Yu. Optimality and Robustness in Statistical Forecasting (in Russian) / Yu. Kharin. — Minsk: BSU, 2008.
3. Huryn, A. Risk of Forecasting of Autoregressive Time Series with Missing Data / A. Huryn // Proceedings of the International Conference “Modern Stochastics: Theory and Applications”, Dedicated to the 60th Anniversary of the Department of Probability Theory and Mathematical Statistics and to the Memory of Professor M.Y. Yadrenko, Kyiv, June 19–23, 2006 / Kyiv National Taras Shevchenko University; editors: V. Buldygin [and others]. — Kyiv, 2006. — P. 139.