Information Worth of MinMaxEnt Models for Time Series
Abstract: In this study, by starting from Maximum entropy (MaxEnt) distribution of time series, we introduce a measure that quantifies information worth of a set of autocovariances. The information worth of autocovariences is measured in terms of entropy difference of MaxEnt distributions subject to different autocovariance sets due to the fact that the information discrepancy between two distributions is measured in terms of their entropy difference in MaxEnt modeling. However, MinMaxEnt distributions (models) are obtained on the basis of MaxEnt distributions dependent on parameters according to autocovariances for time series. This distribution is the one which has minimum entropy and maximum information out of all MaxEnt distributions for family of time series constructed by considering one or several values as parameters. Furthermore, it is shown that as the number of autocovariances increases, the entropy of approximating distribution goes on decreasing. In addition, it is proved that information worth of each model defined on the basis of MinMaxEnt modeling about stationary time series is equal to sum of all possible information increments corresponding to each model with respect to preceding model starting with first model in the sequence of models. The fulfillment of obtained results is demonstrated on an example by using a program written in Matlab.
Cite this paper: Shamilov, A. and Giriftinoglu, C. (2015) Information Worth of MinMaxEnt Models for Time Series. Applied Mathematics, 6, 221-227. doi: 10.4236/am.2015.62021.
References

[1]   Kapur, J.N. and Kesavan, H.K. (1992) Entropy Optimization Principles with Applications. Academic Press, New York.

[2]   Wei, W.S. (2006) Time Series Analysis, Univariate and Multivariate Methods. Pearson, United States.

[3]   Box, G.E.P. and Jenkins, G. (1976) Time Series Analysis: Forecasting and Control. Holden-Day, United States.

[4]   Little, R. and Rubin, D. (1987) Statistical Analysis with Missing Data. Wiley, New York.

[5]   Pourahmadi, M. and Soofi, E. (1998) Prediction Variance and Information Worth of Observations in Time Series. Journal of Time Series Analysis, 21, 413-434.
http://dx.doi.org/10.1111/1467-9892.00191

[6]   Pourahmadi, M. (1989) Estimation and Interpolation of Missing Values of a Stationary Time Series. Journal of Time Series Analysis, 10, 149-169.
http://dx.doi.org/10.1111/j.1467-9892.1989.tb00021.x

[7]   Shamilov, A. (2006) A Development of Entropy Optimization Methods. WSEAS Transaction on Mathematics, 5, 568-575.

[8]   Shamilov, A. (2007) Generalized Entropy Optimization Problems and the Existence of Their Solutions. Physica A: Statistical Mechanics and its Applications, 382, 465-472.
http://dx.doi.org/10.1016/j.physa.2007.04.014

[9]   Shamilov, A. (2010) Generalized Entropy Optimization Problems with Finite Moment Functions Sets. Journal of Statistics and Management Systems, 13, 595-603,.
http://dx.doi.org/10.1080/09720510.2010.10701489

[10]   Shamilov, A. and Giriftinoglu, C. (2010) Generalized Entropy Optimization Distributions Dependent on Parameter in Time Series. WSEAS Transactions on Information Science and Applications, 1, 102-111.

Top