Forward estimation for ergodic time series

Gusztáv Morvai; Benjamin Weiss

doi:10.1016/j.anihpb.2004.07.002

Forward estimation for ergodic time series

Gusztáv Morvai
, Benjamin Weiss^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

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 (X₀,...,X_n) and for which, error (n) = g_n(x) - P (X_n+1= x X₀,..., 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.

Original language	English
Pages (from-to)	859-870
Number of pages	12
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	41
Issue number	5
DOIs	https://doi.org/10.1016/j.anihpb.2004.07.002
State	Published - Sep 2005

Keywords

Nonparametric estimation
Stationary processes

Access to Document

10.1016/j.anihpb.2004.07.002

Cite this

@article{27248fd1b0d6486d95425f2e589b4f97,

title = "Forward estimation for ergodic time series",

abstract = "The forward estimation problem for stationary and ergodic time series \{Xn\}n=0∞ taking values from a finite alphabet X is to estimate the probability that Xn+1 = x based on the observations Xi, 0 ≤ i ≤ n without prior knowledge of the distribution of the process \{Xn\}. We present a simple procedure gn which is evaluated on the data segment (X0,...,Xn) and for which, error (n) = gn(x) - P (Xn+1= x X0,..., Xn) → 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.",

keywords = "Nonparametric estimation, Stationary processes",

author = "Guszt{\'a}v Morvai and Benjamin Weiss",

year = "2005",

month = sep,

doi = "10.1016/j.anihpb.2004.07.002",

language = "אנגלית",

volume = "41",

pages = "859--870",

journal = "Annales de l'institut Henri Poincare (B) Probability and Statistics",

issn = "0246-0203",

publisher = "Institute of Mathematical Statistics",

number = "5",

}

TY - JOUR

T1 - Forward estimation for ergodic time series

AU - Morvai, Gusztáv

AU - Weiss, Benjamin

PY - 2005/9

Y1 - 2005/9

N2 - The forward estimation problem for stationary and ergodic time series {Xn}n=0∞ taking values from a finite alphabet X is to estimate the probability that Xn+1 = x based on the observations Xi, 0 ≤ i ≤ n without prior knowledge of the distribution of the process {Xn}. We present a simple procedure gn which is evaluated on the data segment (X0,...,Xn) and for which, error (n) = gn(x) - P (Xn+1= x X0,..., Xn) → 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.

AB - The forward estimation problem for stationary and ergodic time series {Xn}n=0∞ taking values from a finite alphabet X is to estimate the probability that Xn+1 = x based on the observations Xi, 0 ≤ i ≤ n without prior knowledge of the distribution of the process {Xn}. We present a simple procedure gn which is evaluated on the data segment (X0,...,Xn) and for which, error (n) = gn(x) - P (Xn+1= x X0,..., Xn) → 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.

KW - Nonparametric estimation

KW - Stationary processes

UR - https://www.scopus.com/pages/publications/23944515510

U2 - 10.1016/j.anihpb.2004.07.002

DO - 10.1016/j.anihpb.2004.07.002

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:23944515510

SN - 0246-0203

VL - 41

SP - 859

EP - 870

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 5

ER -

Forward estimation for ergodic time series

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this