On Non-Linear Non-Gaussian Autoregressive Model with Application to Daily Exchange Rate

The most often used distribution in statistical modeling follows Gaussian distribution. But many real-life time series data do not follow normal distribution and assumptions; therefore, inference from such a model could be misleading. Thus, a reparameterized non-Gaussian Autoregressive (NGAR) model that has the capabilities of handling non-Gaussian time series was proposed, while Anderson Darling statistics was used to identify the distribution embedded in the time series. In order to determine the performance of the proposed model, the Nigerian monthly exchange rate (Dollar-Naira Selling Rate) was analyzed using proposed and classical autoregressive models. The proposed model was used to determine the joint distribution of the observed series by separating the marginal distribution from the serial dependence. The maximum Likelihood (MLE) estimation method was used to obtain an optimal solution in estimating the generalized gamma distribution of the proposed model. The selection criteria used in this study were Akaike Information Criterion (AIC). The result revealed through the value of the Anderson Darling statistics that the data set were not normally distributed. The best model was selected using the minimum values of AIC value. The study concluded that the proposed model clearly shows that the non-Gaussian Autoregressive model is a very good alternative for analyzing time series data that deviate from the assumptions of normality and, in particular, for the estimation of its parameters

Decorrelation of Neutral Vector Variables: Theory and Applications

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian distributed, the conventional principal component analysis (PCA) cannot yield mutually independent scalar variables. With the two proposed transformations, a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom. We also evaluate the decorrelation performances for the vectors generated from a single Dirichlet distribution and a mixture of Dirichlet distributions. The mutual independence is verified with the distance correlation measurement. The advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations