论文信息 - AN APPROXIMATED PRINCIPAL COMPONENT PREDICTION MODEL FOR CONTINUOUS-TIME STOCHASTIC PROCESSES

AN APPROXIMATED PRINCIPAL COMPONENT PREDICTION MODEL FOR CONTINUOUS-TIME STOCHASTIC PROCESSES

SUMMARY In this paper, a linear model for forecasting a continuous-time stochastic process in a future interval in terms of its evolution in a past interval is developed. This model is based on linear regression of the principal components in the future against the principal components in the past. In order to approximate the principal factors from discrete observations of a set of regular sample paths, cubic spline interpolation is used. An application for forecasting tourism evolution in Granada is also included. ( 1997 by John Wiley & Sons, Ltd.

Ana M. Aguilera | Mariano J. Valderrama | Francisco A. Ocaña

[1] J. Ramsay,et al. Principal components analysis of sampled functions , 1986 .

[2] O. Bouhaddou,et al. Principal component analysis and interpolation of stochastic processes: methods and simulation , 1987 .

[3] C. L. Chiang,et al. An introduction to stochastic processes and their applications , 1978 .

[4] Jean-Claude Deville. Analyse et prévision des séries chronologiques multiples non stationnaires , 1978 .

[5] Gilbert Saporta,et al. Data analysis for numerical and categorical individual time‐series , 1985 .

[6] Deville. Méthodes statistiques et numériques de l'analyse harmonique , 1974 .

[7] E. A. Sylvestre,et al. Principal modes of variation for processes with continuous sample curves , 1986 .

[8] Ana M. Aguilera,et al. Computational approaches to estimation in the principal component analysis of a stochastic process , 1995 .

[9] J. Ramsay,et al. Some Tools for Functional Data Analysis , 1991 .

[10] J. E. Jackson. A User's Guide to Principal Components , 1991 .

[11] P. Besse. Approximation spline de l'analyse en composantes principales d'une variable aléatoire hilbertienne , 1991 .