Limits to consistent on-line forecasting for ergodic time series

Györfi, László; Morvai, Gusztáv; Yakowitz, S.

doi:10.1109/18.661540

Cited by 61 publications

(62 citation statements)

References 13 publications

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“…We note that from the proof of Ryabko [22] and Györfi, Morvai, Yakowitz [11] it is clear that the continuity condition in the first part of the Theorem can not be relaxed. Even for the class of all stationary and ergodic binary timeseries with merely almost surely continuous conditional probability P (X 1 = 1| .…”

Section: Preliminaries and Main Resultsmentioning

confidence: 99%

“…Indeed, whenever a new state appears which has not occured before, you are unable to predict, cf. Györfi, Morvai, Yakowitz [11].…”

Section: Preliminaries and Main Resultsmentioning

confidence: 99%

“…This problem was answered by Bailey [5] in a negative way, that is, he showed that there is no such scheme. (Also see Ryabko [22], Györfi, Morvai, Yakowitz [11] and Weiss [24].) Bailey used the technique of cutting and stacking developed by Ornstein [21] and Shields [23].…”

Section: Problemmentioning

confidence: 99%

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Forward estimation for ergodic time series

Morvai

Weiss

2005

Annales de l'Institut Henri Poincare (B) Probability and Statis

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The forward estimation problem for stationary and ergodic time series {X n } ∞ n=0 taking values from a finite alphabet X is to estimate the probability that X n+1 = x based on the observations X i , 0 ≤ i ≤ n without prior knowledge of the distribution of the process {X n }. We present a simple procedure g n which is evaluated on the data segment (X 0 , . . . , X n ) and for which, error(n) = |g n (x) − P (X n+1 = x|X 0 , . . . , X n )| → 0 almost surely for a subclass of all stationary and ergodic time series, while for the full class the Cesaro average of the error tends to zero almost surely and moreover, the error tends to zero in probability.Le problème d'estimation future d'une série de temps ergodique et stationnaire {X n } ∞ n=0 , qui prend ses valeures dans un alphabet fini X , est d'estimer la probabilité que X n+1 = x, connaissant les X i pour 0 ≤ i ≤ n mais sans connaissance préalable de la distribution du processus {X i }. Nous présentons un procédé simple g n , evalué dur les données (X 0 , . . . , X n ), pour lequel erreur(n) = |g n (x) − P (X n+1 = x|X 0 , . . . , X n ) → 0 presque sûrement pour une sous-classe de toutes les séries de temps ergodiques et stationnaires, tandis que pour la classe entière la moyenne de Cesaro de l'erreur tend vers zéro presque sûrement. De plus, l'erreur tend vers zéro en probabilité.

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Section: Preliminaries and Main Resultsmentioning

confidence: 99%

“…Indeed, whenever a new state appears which has not occured before, you are unable to predict, cf. Györfi, Morvai, Yakowitz [11].…”

Section: Preliminaries and Main Resultsmentioning

confidence: 99%

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Forward estimation for ergodic time series

Morvai

Weiss

2005

Annales de l'Institut Henri Poincare (B) Probability and Statis

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“…We emphasize that without (A7) the partitioning estimate is not consistent Gyorfi etal. [18,Theorem 2]. Note that the assumption (A7) holds when, for instance, we take Yi -X i+l and {X,} a Markov process.…”

Section: Theorem 1 Suppose That (X T Yi) Satisfies the Assumptionsmentioning

confidence: 99%

“…See, for instance, Yakowitz [34], Gyorfi and Masry [17], Tran [30], Roussas [29], Laib [22] and Bosq [3]. The monograph by Gyorfi et al [18] gives a large coverage of the literature in nonparametric inference for dependent series. Our aim in this paper is to prove the uniform almost sure convergence of the partitioning estimate, which is a histogram-like mean regression function, under very weak assumptions on the dependence structure of the vector of random variable Z = (X, Y).…”

Section: Introductionmentioning

confidence: 99%

Uniform consistency of the partitioning estimate under ergodic conditions

Laïb

1999

J Aust Math Soc A

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We establish the uniform almost sure convergence of the partitioning estimate, which is a histogram-like mean regression function estimate, under ergodic conditions for a stationary and unbounded process. The main application of our results concerns time series analysis and prediction in the Markov processes case.1991 Mathematics subject classification (Amer. Math. Soc): primary 62G05; secondary 60F15, 62M10.

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Universal prediction and universal coding

Suzuki

2003

Systems & Computers in Japan

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SUMMARYAlthough prediction schemes called "universal" are now abundant, very little attention has been devoted to the definition of universal prediction. This paper addresses, for α-nary (α ≥ 2) sequences, the criteria of successful universal prediction and the prediction schemes that achieve the goals. We propose the following criteria: for any probability measures in a given measure class, the error probability of prediction (in the problem of predicting a value for the next outcome) and the conditional probability of the next outcome given the past sequence (in the problem of predicting a probability distribution for the next outcome, i.e., the probability assignment problem) should converge to the optimal values in probability (weakly universal) and almost surely (strongly universal). We present a small review of various results on universal prediction, and give several results relating the developed criteria to each other and to various prediction submeasures. Furthermore, we explore the connection between universal prediction and universal coding. The proposed criteria are applied to any measure class as well as stationary ergodic measures.

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Limits to consistent on-line forecasting for ergodic time series

Cited by 61 publications

References 13 publications

Forward estimation for ergodic time series

Forward estimation for ergodic time series

Uniform consistency of the partitioning estimate under ergodic conditions

Universal prediction and universal coding

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