INCREMENT-VECTOR METHODOLOGY - TRANSFORMING NONSTATIONARY SERIES TO STATIONARY SERIES

In time series analysis, it is well-known that the differencing operat or del(d) may transform a non-stationary series, {Z(t)} say, to a stat ionary one, {W(t) = del(d)Z(t)}; and there are many procedures for ana lysing and modelling {Z(t)} which exploit this transformation. Rather differently, Matheron (1973) introduced a set of measures on R-n that transform an appropriate non-stationary spatial process to stationarit y, and Cressie (1988) then suggested that specialized low-order analog ues of these measures, called increment-vectors, be used in time serie s analysis. This paper develops a general theory of increment-vectors which provides a more powerful transformation tool than mere simple di fferencing. The methodology gives a handle on the second-moment struct ure and divergence behaviour of homogeneously non-stationary series wh ich leads to many important applications such as determining the corre ct degree of differencing, forecasting and interpolation.