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September, 1982 Time Series Discrimination by Higher Order Crossings
Benjamin Kedem, Eric Slud
Ann. Statist. 10(3): 786-794 (September, 1982). DOI: 10.1214/aos/1176345871


A new methodology is proposed for discrimination among stationary time-series. The time series are transformed into binary arrays by clipping (retaining only the signs of) the $j$th difference series, $j = 0, 1, 2, \cdots$. The degeneracy of clipped $j$th differences is studied as $j$ becomes large. A new goodness of fit statistic is defined as a quadratic form in the counts of axis-crossings by each of the first $k$ differences of the series. Simulations and the degeneracy of high-order differences justify fixing $k$ no larger than 10 for many processes. Empirical simulated distributions (with $k = 9$) of the goodness of fit statistic suggest a gamma approximation for its tail probabilities. Illustrations are given of discrimination between simple models with the new statistic.


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Benjamin Kedem. Eric Slud. "Time Series Discrimination by Higher Order Crossings." Ann. Statist. 10 (3) 786 - 794, September, 1982.


Published: September, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0515.62084
MathSciNet: MR663432
Digital Object Identifier: 10.1214/aos/1176345871

Primary: 62M10
Secondary: 62H30 , 62M07

Keywords: clipped signal , discrimination , goodness of fit , higher-order crossings , level crossings , stationary time series

Rights: Copyright © 1982 Institute of Mathematical Statistics


Vol.10 • No. 3 • September, 1982
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