Entropy optimization methods in time series

In this thesis, via Maximum Entropy Method under the assumption that the number of exact autocovariances for time series is known, the acceptability of MaxEnt Distributions with autocovariances beyond the lag is investigated by virtue of Jaynes?s concentration theorem. It is proposed that the process for acceptability of MaxEnt Distributions can be also used to determine lag number and to estimate parameters of autoregressive model. Moreover, it is given that the formulation of Generalized Entropy Optimization Problem (GEOP) which requires obtaining distribution represents given statistical data in the best form and it is shown that MinMaxEnt and MaxMaxEnt Distributions are a solution of this problem. Later, MinMaxEnt and MaxMaxEnt for MaxEnt Distributions with moment functions and moment values dependent on parameter are defined, these distributions are found for the time series with missing values. By means of relations established between entropy values of MaxEnt, MinMaxEnt and MaxMaxEnt distributions, it is proved that the distribution containing the largest information is MinMaxEnt distribution. Through the result, estimating of missing and feature value is considered respectively as a problem and a method based on MinMaxEnt distribution is developed for solving these problems. The computations are performed by the programmes written in Matlab in order to use the developed method according to the number of forecast and missing values. The performance of the developed method is evaluated by mean square errors (MSE) calculated from simulations for different number of missing values on the time series generated by models with lag one, two, three and four. Furthermore, MSE?s are calculated from simulation studies by using mentioned method for one, two and more forecasting and the validity of this method is shown.