A Graphical Similarity Measure for Time Series Models.
Abstract
The purpose of this document is to introduce a graphical device useful as a measure of similarity or as a goodness of fit criterion for hypothesized time series models. It is based on the actual oscillation observed in time series as depicted by axis-crossings and higher order crossings. Higher order crossings (HOC) are axis-crossings of differenced time series and are closely linked to the spectral content of the series. In fact under the Gaussian assumption, to which we shall adhere, HOC determine the finite dimensional distributions up to a scale parameter given that the mean is zero. The main advantage of HOC is that they are easily obtained from an observed series and that only very few of them are needed, as the dicriminatory power in HOC usually diminishes with their order. Higher order crossings in time series discrimination were discussed in Kedem and Slud (1981), (1982), where a certain goodness of fit criterion is suggested, Here however the emphasis is on a graphical device rather than a single test statistic. This graphical method may be shown useful in answering the question 'Does a given time series oscillate as a certain hypothesized model?' Some examples with real and simulated data demonstrate the use and potential of this method.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1985
- Accession Number
- ADA158869
Entities
People
- B. Kedem
Organizations
- University of Maryland