Abstract
The classical autocorrelation function may not be an effective and informative means in revealing the dependence features of a binary time series {yt}. Recently, the autopersistence functions defined as APF0(k) = P(yt+k = 1 | yt = 0) and APF1(k) = P(yt+k = 1 | yt = 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. Copyright © 2011 Blackwell Publishing Ltd.
Original language | English |
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Pages (from-to) | 639-646 |
Journal | Journal of Time Series Analysis |
Volume | 32 |
Issue number | 6 |
Early online date | Mar 2011 |
DOIs | |
Publication status | Published - Nov 2011 |
Citation
Wang, C., & Li, W. K. (2011). On the autopersistence functions and the autopersistence graphs of binary autoregressive time series. Journal of Time Series Analysis, 32(6), 639-646. doi: 10.1111/j.1467-9892.2011.00721.xKeywords
- Autopersistence function
- Autopersistence graph
- Binary time series
- Markov chain
- Consistency
- Asymptotic normality