Forecasting for Stationary Binary Time Series

Gusztáv Morvai*, Benjamin Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

The forecasting problem for a stationary and ergodic binary time series {Xn}n=0 is to estimate the probability that Xn+1 = 1 based on the observations Xi, 0 ≤ i ≤ n without prior knowledge of the distribution of the process {Xn}. It is known that this is not possible if one estimates at all values of n. We present a simple procedure which will attempt to make such a prediction infinitely often at carefully selected stopping times chosen by the algorithm. We show that the proposed procedure is consistent under certain conditions, and we estimate the growth rate of the stopping times.

Original languageEnglish
Pages (from-to)25-34
Number of pages10
JournalActa Applicandae Mathematicae
Volume79
Issue number1-2
DOIs
StatePublished - Oct 2003

Keywords

  • Nonparametric estimation
  • Stationary processes

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