Forward estimation for ergodic time series

 Access to full text

 Full (PDF)

1. [1] P. Algoet, Universal schemes for prediction, gambling and portfolio selection, Ann. Probab.20 (1992) 901-941, Correction, Ann. Probab.23 (1995) 474-478. Zbl0758.90006MR1159579
2. [2] P. Algoet, The strong low of large numbers for sequential decisions under uncertainty, IEEE Trans. Inform. Theory40 (1994) 609-634. Zbl0827.62077MR1295308
3. [3] P. Algoet, Universal schemes for learning the best nonlinear predictor given the infinite past and side information, IEEE Trans. Inform. Theory45 (1999) 1165-1185. Zbl0959.62078MR1686250
4. [4] K. Azuma, Weighted sums of certain dependent random variables, Tohoku Math. J.37 (1967) 357-367. Zbl0178.21103MR221571
5. [5] D.H. Bailey, Sequential Schemes for Classifying and Predicting Ergodic Processes, Ph.D. thesis, Stanford University, 1976. 
6. [6] T.M. Cover, Open problems in information theory, in: 1975 IEEE Joint Workshop on Information Theory, IEEE Press, New York, 1975, pp. 35-36. MR469507
7. [7] R.M. Gray, Probability, Random Processes, and Ergodic Properties, Springer-Verlag, New York, 1988. Zbl0644.60001MR918767
8. [8] L. Györfi, M. Kohler, A. Krzyżak, H. Walk, A Distribution Free Theory of Nonparametric Regression, Springer-Verlag, New York, 2002. Zbl1021.62024MR1920390
9. [9] L. Györfi, G. Lugosi, Strategies for sequential prediction of stationary time series, in: Dror M., L'Ecuyer P., Szidarovszky F. (Eds.), Modeling Uncertainty an Examination of Stochastic Theory, Methods, and Applications, Kluwer Academic, 2002, pp. 225-248. MR1893282
10. [10] L. Györfi, G. Lugosi, G. Morvai, A simple randomized algorithm for consistent sequential prediction of ergodic time series, IEEE Trans. Inform. Theory45 (1999) 2642-2650. Zbl0951.62080MR1725166
11. [11] L. Györfi, G. Morvai, S. Yakowitz, Limits to consistent on-line forecasting for ergodic time series, IEEE Trans. Inform. Theory44 (1998) 886-892. Zbl0899.62122MR1607704
12. [12] S. Kalikow, Random Markov processes and uniform martingales, Israel J. Math.71 (1990) 33-54. Zbl0711.60041MR1074503
13. [13] M. Keane, Strongly mixing g-measures, Invent. Math.16 (1972) 309-324. Zbl0241.28014MR310193
14. [14] Ph.T. Maker, The ergodic theorem for a sequence of functions, Duke Math. J.6 (1940) 27-30. Zbl0027.07705MR2028JFM66.1286.01
15. [15] G. Morvai, Estimation of conditional distribution for stationary time series, Ph.D. thesis, Technical University of Budapest, 1994. 
16. [16] G. Morvai, Guessing the output of a stationary binary time series, in: Haitovsky Y., Lerche H.R., Ritov Y. (Eds.), Foundations of Statistical Inference, Physika-Verlag, 2003, pp. 207-215. Zbl05280104MR2017826
17. [17] G. Morvai, B. Weiss, Forecasting for stationary binary time series, Acta Appl. Math.79 (2003) 25-34. Zbl1030.62076MR2021874
18. [18] G. Morvai, S. Yakowitz, P. Algoet, Weakly convergent nonparametric forecasting of stationary time series, IEEE Trans. Inform. Theory43 (1997) 483-498. Zbl0871.62082MR1447529
19. [19] G. Morvai, S. Yakowitz, L. Györfi, Nonparametric inferences for ergodic, stationary time series, Ann. Statist.24 (1996) 370-379. Zbl0855.62076MR1389896
20. [20] D.S. Ornstein, Guessing the next output of a stationary process, Israel J. Math.30 (1978) 292-296. Zbl0386.60032MR508271
21. [21] D.S. Ornstein, Ergodic Theory, Randomness, and Dynamical Systems, Yale University Press, 1974. Zbl0296.28016MR447525
22. [22] B.Ya. Ryabko, Prediction of random sequences and universal coding, Problems Inform. Transmission24 (April–June 1988) 87-96. Zbl0666.94009MR955983
23. [23] P.C. Shields, Cutting and stacking: a method for constructing stationary processes, IEEE Trans. Inform. Theory37 (1991) 1605-1614. Zbl0741.94007MR1134300
24. [24] B. Weiss, Single Orbit Dynamics, American Mathematical Society, 2000. Zbl1083.37500MR1727510

1. Gusztáv Morvai, Benjamin Weiss, Intermittent estimation for finite alphabet finitarily Markovian processes with exponential tails