Estimation of Time -Varying Linear Regression with Unknown Time -Volatility via Continuous Generalization of the Akaike Information Criterion
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:52203", author = "Elena Ezhova and Vadim Mottl and Olga Krasotkina", title = "Estimation of Time -Varying Linear Regression with Unknown Time -Volatility via Continuous Generalization of the Akaike Information Criterion", abstract = "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.", volume = "3", number = "3", pages = "198-6", }