Forecasting Time Series by Functional Pca. Discussion of Several Weighted Approaches

In this paper a functional principal component model is applied to forecast a continuous time series that has been observed only at discrete time points not necessarily equally spaced. To take into account the natural order among the sample paths obtained after cutting the series into pieces, a weighted estimation of the principal components is proposed. In order to estimate the weighted functional principal component analysis, a cubic spline interpolation of the sample paths between their discrete observations is performed. Finally, an application with stimulated data is developed where model fitting and forecasting results using different types of weightings on equally and unequally spaced data are given and discussed. The forecasting performance of the estimated functional principal component models is also compared with multivariate principal component regression models