On Non-Linear Non-Gaussian Autoregressive Model with Application to Daily Exchange Rate
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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.
Keywords
QA Mathematics