Alternative Method for the Estimation of Parameters for the Normal Inverse Gaussian Distribution

Abstract

This article presents a study on the parameter estimation of the Normal Inverse Gaussian distribution, which is a specialized instance of the generalized hyperbolic distribution that is extensively utilized in the analysis of financial time series. Conventionally, the maximum likelihood method and the method of moment are used to estimate the parameters; however, these methods have a restriction on the feasible domain of possible skewness and excess kurtosis values. Therefore, we propose an alternative parameter estimation method for the Normal Inverse Gaussian distribution based on the Metropolis Hasting exponential maximum likelihood method. Moreover, the performance of this method will be compared with the maximum likelihood estimator, the epsilon maximum likelihood estimator, the exponential maximum likelihood estimator, and the Metropolis Hasting maximum likelihood estimator using both simulated and real-world datasets. For simulation, we use the smallest root mean square error and provide descriptive statistics, including means and standard deviations to evaluate the performance of the model. For real data application, the selection of the model is guided by a goodness-of-fit test using the Anderson-Darling test statistics criterion. Furthermore, the model selection should demonstrate the smallest AD value alongside the highest p-value.