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Increment-Vector Methodology: Transforming Non-Stationary Series to Stationary Series

Part of: Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Zhao-Guo Chen  and
Oliver D. Anderson
Zhao-Guo Chen*
Affiliation:
Statistics Canada
*
∗Postal address: Time Series Research and Analysis Centre, 3H, R.H. Coats Building, Statistics Canada, Ottawa, Ontario, Canada K1A 0T6
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Abstract

In time series analysis, it is well-known that the differencing operator ∇d may transform a non-stationary series, {Z(t)} say, to a stationary one, {W(t)} = ∇dZ(t)}; and there are many procedures for analysing and modelling {Z(t)} which exploit this transformation. Rather differently, Matheron (1973) introduced a set of measures on Rn that transform an appropriate non-stationary spatial process to stationarity, and Cressie (1988) then suggested that specialized low-order analogues of these measures, called increment-vectors, be used in time series analysis. This paper develops a general theory of increment-vectors which provides a more powerful transformation tool than mere simple differencing. The methodology gives a handle on the second-moment structure and divergence behaviour of homogeneously non-stationary series which leads to many important applications such as determining the correct degree of differencing, forecasting and interpolation.

Keywords

ARIMA modeldegree of differencingdifference equationsgeneralized covariance functiongeneralized differencing operatorintegrated stationary time seriesintrinsic random functionpolyvariogramvariogram

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998 , pp. 64 - 77
Copyright
Copyright © Applied Probability Trust 1998 

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