Curve Forecasting by Functional Autoregression
AbstractData 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 reducedrank 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.
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Bibliographic InfoPaper provided by Columbia University, Department of Economics in its series Discussion Papers with number 0405-18.
Length: 36 pages
Date of creation: 2004
Date of revision:
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Other versions of this item:
- C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Longitudinal Data; Spatial Time Series
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
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