GARIMA FIRST-ORDER AUTOREGRESSIVE PROCESS: PROPERTIES, ESTIMATION METHODS AND APPLICATION

Abstract

A new stationary autoregressive process with the Garima marginal distribution is introduced in this paper. Properties of the model such as the distribution of the corresponding error term, conditional moments, time irreversibility, autocorrelation function, spectral density and run probabilities are extensively studied. A simulation study is carried out to compare the performance of the Yule-Walker, conditional least squares and Gaussian estimation procedures in estimating the parameters of the new model. The simulation results indicate that the Gaussian estimation technique is the best among the three methods. The fit of the model to German bilateral real exchange rate data is compared with fits of three existing AR(1) models namely, Gaussian, Exponential and Lindley AR(1) models using Akaike information criterion (AIC) and Bayesian information criterion (BIC). The proposed model is found to be the best for modeling the data among the fitted models since it corresponds to the smallest value of the AIC and BIC.