Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes
Journal of Multivariate Analysis
Testing the stability of the functional autoregressive process
Journal of Multivariate Analysis
Some research on functional data analysis
ICSI'10 Proceedings of the First international conference on Advances in Swarm Intelligence - Volume Part II
Detecting changes in functional linear models
Journal of Multivariate Analysis
Test of independence for functional data
Journal of Multivariate Analysis
Conditional estimation for dependent functional data
Journal of Multivariate Analysis
Computing the best linear predictor in a Hilbert space. Applications to general ARMAH processes
Journal of Multivariate Analysis
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This paper deals with the prediction of curve-valued autoregression processes. It develops a novel technique, predictive factor decomposition, for the estimation of the autoregression operator. The technique is based on finding a reduced-rank approximation to the autoregression operator that minimizes the expected squared norm of the prediction error. Implementing this idea, we relate the operator approximation problem to the singular value decomposition of a combination of cross-covariance and covariance operators. We develop an estimation method based on regularization of the empirical counterpart of this singular value decomposition, prove its consistency and evaluate convergence rates. The method is illustrated by an example of the term structure of the Eurodollar futures rates. In the sample corresponding to the period of normal growth, the predictive factor technique outperforms the principal components method and performs on a par with custom-designed prediction methods.