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Estimation of Time -Varying Linear Regression with Unknown Time -Volatility via Continuous Generalization of the Akaike Information Criterion

Authors: Elena Ezhova, Vadim Mottl, Olga Krasotkina


The problem of estimating time-varying regression is inevitably concerned with the necessity to choose the appropriate level of model volatility - ranging from the full stationarity of instant regression models to their absolute independence of each other. In the stationary case the number of regression coefficients to be estimated equals that of regressors, whereas the absence of any smoothness assumptions augments the dimension of the unknown vector by the factor of the time-series length. The Akaike Information Criterion is a commonly adopted means of adjusting a model to the given data set within a succession of nested parametric model classes, but its crucial restriction is that the classes are rigidly defined by the growing integer-valued dimension of the unknown vector. To make the Kullback information maximization principle underlying the classical AIC applicable to the problem of time-varying regression estimation, we extend it onto a wider class of data models in which the dimension of the parameter is fixed, but the freedom of its values is softly constrained by a family of continuously nested a priori probability distributions.

Keywords: Time varying regression, time-volatility of regression coefficients, Akaike Information Criterion (AIC), Kullback information maximization principle

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[1] Akaike H. A new look at the statistical model idendification. IEEE Trans. on Automatic Control, Vol. IC-19, No.6, December 1974, pp. 716-723.
[2] Kitagawa G., Akaike H. A procedure for the modeling of no-stationary time series. Ann. Inst. Statist. Math., Vol. 30, Part B, 1987, pp. 351-363.
[3] Scharz G. Estimating the dimtnsion of the model. The Annals of Statistics, Vol. 6,No.2, 1978, pp. 461-464.
[4] Bozdogan H. Model selection and Akaike-s Information Criterion (AIC): The general theory and its analytical extensions. Psychometrica, Vol. 52, No.3, September 1987.
[5] Spiegelhalter D., Best N., Carlin B. Van der Linde A. Bayesian mesures of model complexity and fit. Journal of the Royal Statistical Society. Series B (Statistical Methodology), Vol. 64, No.4, 2002, pp. 583-639.
[6] Rodrigues C.C. The ABC of model selection: AIC, BIC and new CIC. AIP Conference Proceedings, Vol. 803, November 23, 2005, pp. 80-87.
[7] Markov M., Krasotkina O., Mottl V., Muchnik I. Time-varying regression model with unknown time-volatility for nonstationary signal analyses. Proceedings of the 8th IASTED Internation Conference on Signal and Image Processing. Honolulu, Hawaii, USA, August 14-16, 2006.
[8] Markov M., Muchnik I., Mottl V., Krasotkina O. Dynamic analysis of hedge funds. Proceedings of the 3rd IASTED Internation Conference on Financal Engineering and Applications. Cambridge, Massachusetts, USA, October 9-11, 2006.
[9] Bishop C.M. Pattern Recognition and Machine Learning. Springer, 2006.