Aguilera, Ana M.; Ocana, Francisco A.; Valderrama, Mariano J. An approximated principal component prediction model for continuous time stochastic processes. (English) Zbl 0885.62109 Appl. Stochastic Models Data Anal. 13, No. 2, 61-72 (1997). Let \(X(t)\) be a stochastic process with \(E[X(t)]=0\). This article deals with a linear model for forecasting of \(X(t)\) on the interval \([T_{3},T_{4}]\) in terms of its evolution on the interval \([T_1,T_2], \;T_2<T_3\). The authors propose the principal components prediction model for the process \(X(t)\) for \(t\in [T_3,T_4]\) in the form \(\tilde X^{q}(t)= \sum\limits_{j=1}^{q}\tilde\eta_{j}^{p_{j}}g_{j}(t)\), where \(\eta_{j}^{p_{j}}\) are the truncated least squares linear estimates of the principal components \(\eta_{j}\), \(g_{j}(t)\) are the principal factors on the interval \([T_3,T_4]\). In order to approximate the principal factors from discrete observations of a set of regular sample paths, cubic spline interpolation is used. This model is used for forecasting tourism evolution in Spanish cities. Reviewer: A.D.Borisenko (Kyïv) Cited in 14 Documents MSC: 62M20 Inference from stochastic processes and prediction 62H25 Factor analysis and principal components; correspondence analysis 60J25 Continuous-time Markov processes on general state spaces Keywords:principal components; Karhunen-Loeve expansion; least squares linear prediction; cubic \(B\)-splines PDFBibTeX XMLCite \textit{A. M. Aguilera} et al., Appl. Stochastic Models Data Anal. 13, No. 2, 61--72 (1997; Zbl 0885.62109) Full Text: DOI