Curve Forecasting by Functional Autoregression

Alexei Onatski () and V. Karguine

No 59, Computing in Economics and Finance 2005 from Society for Computational Economics

Abstract: Data in which each observation is a curve occur in many applied problems. This paper explores prediction in time series in which the data is generated by a curve-valued autoregression process. It develops a novel technique, the predictive factor decomposition, for estimation of the autoregression operator, which is designed to be better suited for prediction purposes than the principal components method. The technique is based on finding a reduced-rank approximation to the autoregression operator that minimizes the norm of the expected prediction error. Implementing this idea, we relate the operator approximation problem to an eigenvalue problem for an operator pencil that is formed by the cross-covariance and covariance operators of the autoregressive process. We develop an estimation method based on regularization of the empirical counterpart of this eigenvalue problem, and prove that with a certain choice of parameters, the method consistently estimates the predictive factors. In addition, we show that forecasts based on the estimated predictive factors converge in probability to the optimal forecasts. The new method is illustrated by an analysis of the dynamics of the term structure of Eurodollar futures rates. We restrict the sample to the period of normal growth and find that in this subsample the predictive factor technique not only outperforms the principal components method but also performs on par with the best available prediction methods

Keywords: Functional data analysis; Dimension reduction, Reduced-rank regression; Principal component; Predictive factor, Generalized eigenvalue problem; Term structure; Interest rates (search for similar items in EconPapers)
JEL-codes: C23 C53 E43 (search for similar items in EconPapers)
Date: 2005-11-11
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-for and nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Journal Article: Curve forecasting by functional autoregression (2008)
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