## The Annals of Statistics

### Time Series Discrimination by Higher Order Crossings

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 10, Number 3 (1982), 786-794.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345871

Digital Object Identifier
doi:10.1214/aos/1176345871

Mathematical Reviews number (MathSciNet)
MR663432

Zentralblatt MATH identifier
0515.62084

JSTOR