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On the autopersistence functions and the autopersistence graphs of binary autoregressive time series
Author(s) -
Wang Chao,
Li Wai Keung
Publication year - 2011
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2011.00721.x
Subject(s) - autocorrelation , mathematics , autoregressive model , partial autocorrelation function , series (stratigraphy) , binary number , function (biology) , time series , statistics , autoregressive integrated moving average , arithmetic , paleontology , evolutionary biology , biology
The classical autocorrelation function may not be an effective and informative means in revealing the dependence features of a binary time series { y t }. Recently, the autopersistence functions defined as APF 0 ( k ) = P ( y t + k = 1 | y t = 0) and APF 1 ( k ) = P ( y t + k = 1 | y t = 1), k = 1, 2,…, have been proposed as alternatives to the autocorrelation function for binary time series. In this article we consider the theoretical autopersistence functions and their natural sample analogues, the autopersistence graphs, under a binary autoregressive model framework. Some properties of the autopersistence functions and the asymptotic properties of the autopersistence graphs are discussed. The results have potential application in the modelling of binary time series.