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An approximated principal component prediction model for continuous time stochastic processes. (English) Zbl 0885.62109

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.

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
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