Modeling Power Exponential Error Innovations with Autoregressive Process (Published)
The regular gussian assumption of the error terms is employed in dynamic time series models when the underlying data are not normally distributed, this often results in incorrect parameter estimations and forecast error. As a result, this paper developed maximum likelihood method of estimation of parameters of an autoregressive model of order 2 [AR (2)] with power-exponential innovations. The performance of the parameters of AR (2) in comparison to normal error innovations was evaluated using the Akaike information criterion (AIC) and forecast performance metrics (RMSE and MAE). Both real data sets and simulated data with different sample sizes were used to validate the models. The results revealed that, it is more appropriate and efficient to model non-normal time series data using AR (2) exponential power error innovations.
Keywords: Innovations, Maximum Likelihood Estimation, autoregressive process, power exponential.
A Study on The Mixture of Exponentiated-Weibull Distribution PART I (The Method of Maximum Likelihood Estimation) (Published)
Mixtures of measures or distributions occur frequently in the theory and applications of probability and statistics. In the simplest case it may, for example, be reasonable to assume that one is dealing with the mixture in given proportions of a finite number of normal populations with different means or variances. The mixture parameter may also be denumerable infinite, as in the theory of sums of a random number of random variables, or continuous, as in the compound Poisson distribution. The use of finite mixture distributions, to control for unobserved heterogeneity, has become increasingly popular among those estimating dynamic discrete choice models. One of the barriers to using mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive reparability of the log likelihood function. In this thesis, the maximum likelihood estimators have been obtained for the parameters of the mixture of exponentiated Weibull distribution when sample is available from censoring scheme.The maximum likelihood estimators of the parameters and the asymptotic variance covariance matrix have been obtained. A numerical illustration for these new results is given.
Keywords: Exponentiated Weibull Distributiom (EW), Maximum Likelihood Estimation, Mixture Distribution, Mixture of two Exponentiated Weibull Distribution(MTEW), Moment Estimation, Monte-Carlo Simulation