Autoregressive moving-average time series model with errors following a log-logistic distribution

Reihaninia, Behzad; Hormozinejad, Farshin; Khodamoradi, Mohammad; Ghalani, Mohammad Reza

doi:10.21608/cjmss.2025.391763.1200

Autoregressive moving-average time series model with errors following a log-logistic distribution

Document Type : Original Article

Authors

¹ Department of statistics, Ahv.C., Islamic Azad University, Ahvaz 61349, Iran

² Department of statistics, Iz.C., Islamic Azad University, Izeh 64171, Iran

10.21608/cjmss.2025.391763.1200

Abstract

In the class of time series' models, the errors of the fitted models may follow a Log-Logistic distribution instead of the Normal distribution. This new model is called the Log-Logistic Autoregressive Moving-Average(L-LARMA) model. Following the introduction of this model's structure, its parameters have been estimated using numerical methods and the conditional maximum likelihood function. The structure for hypothesis testing, the information matrix, and the forecast function have also been developed and described. One application of this model is the forecasting and modeling of the overall stock market index. The overall index is one of the most critical indicators that economists and researchers in the field of economics closely monitor. The model and its forecast function have been fitted and determined using simulation and actual data of Iran stock market index from 2008 to 2022.and actual data of the Iran stock market index from 2008 to 2022. In the final of our paper, we will explain some conclusions and results by using simulation and actual data.

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