On a Weighted Principal Component Model to Forecast a Continuous Time Series

Abstract

In many real life situations information about a continuous time series is given by discrete-time observations not always evenly spaced. Our purpose is to develop a forecasting model for such a time series avoiding some of the restrictive hypotheses imposed by classical approaches. If the original series x(t) is cut in periods of amplitude h (h > 0) then the following process is obtained by rescaling

$$\left\{ {{X_w}\left( t \right) = x\left( {\left( {w - 1} \right)h + t} \right):t \in \left[ {T,\,T + h} \right];\,w = 1,2,....} \right\}.$$

(1)

The forecasting model proposed in this paper is based on linear regression of the principal components (p.c.’s) associated to the process X(t) in the future against its p.c.’s in the past. This research was supported in part by Project PS94-0136 of DGICYT, Ministerio de Educación y Ciencia, Spain