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

Published online by Cambridge University Press:  14 July 2016

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

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1998 

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