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Curve Forecasting by Functional Autoregression

  • A. Onatski
  • V. Karguine

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

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 59.

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Date of creation: 11 Nov 2005
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Handle: RePEc:sce:scecf5:59
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  1. Arnold Wollenberg, 1977. "Redundancy analysis an alternative for canonical correlation analysis," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 207-219, June.
  2. Francis X. Diebold & Canlin Li, 2003. "Forecasting the Term Structure of Government Bond Yields," NBER Working Papers 10048, National Bureau of Economic Research, Inc.
  3. Jean Fortier, 1966. "Simultaneous nonlinear prediction," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 447-455, December.
  4. David Jamieson Bolder & Scott Gusba, 2002. "Exponentials, Polynomials, and Fourier Series: More Yield Curve Modelling at the Bank of Canada," Staff Working Papers 02-29, Bank of Canada.
  5. Antoniadis, Anestis & Sapatinas, Theofanis, 2003. "Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 133-158, October.
  6. Robert R. Bliss, 1997. "Movements in the term structure of interest rates," Economic Review, Federal Reserve Bank of Atlanta, issue Q 4, pages 16-33.
  7. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
  8. Jean Fortier, 1966. "Simultaneous linear prediction," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 369-381, September.
  9. Philippe C. Besse, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 673-687.
  10. He, Guozhong & Müller, Hans-Georg & Wang, Jane-Ling, 2003. "Functional canonical analysis for square integrable stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 54-77, April.
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