Estimate the parameters of the ARMA model when the random error follows a Lindley distribution

Abstract

 This research deals with one of the types of models suggested by Box Jenkins, which is the mixed model ARMA (1,1). Which can deal with time series, whether stable or unstable. The model was reviewed and its functions defined when the random error follows the abnormal distribution, and the Lindley distribution, which is one of the continuous distributions, was used. Appropriate tests were presented for the study and the parameters of the ARMA (1,1) model were estimated by the greatest possible method. The parameters of the Landley distribution were also estimated using the (MLS) method. On the applied side, a set of real data was analyzed that represents the flow of water in one of the rivers of the United Kingdom, where it was found appropriate Distribution of the data and verify that the series is stable, and in diagnosing the model, it was found that the proposed model is ARMA (1,1).