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Statistical Inference in the First-Order Autoregressive-Moving Average Models with Skewed Non-Negative Innovations
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Maryam Kasraie1   , Abdolreza Sayyareh 2 |
1- Islamic Azad University
2- K. N. Toosi University of Technology , asayyareh@khntu.ac.ir |
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Abstract: (1749 Views) |
The most critical assumption in the autoregressive-moving average models (ARMA) is that innovations involved in the modeling process are normally distributed. Nonetheless, in some trials, we encounter instances where the normality assumption of the innovations is violated. In this article we were interested in model selection among the ARMA(1,1) models with innovations from the Weibull and exponential families. This may be beneficial for both forecasting and modeling perspectives. For this purpose, the innovation distribution parameters and the model coefficients were estimated by modified maximum likelihood (MML) method. Afterward, the asymptotic distribution of the acquired estimators in stationary mode was evaluated. Based on a simulation study, the ability of different model selection methods has been compared. Using the simulation, it was demonstrated that Vuong test correctly selected the optimal ARMA(1,1) model with non-negative innovations. Sometimes two competing models were picked as equivalent by the Vuong test. However, it did not indicate that they were close to the true model or away from it. Therefore, we used the Cox test to find out if the equivalent models are suitable or unsuitable. The obtained results of the tracking intervals has confirmed the results of the Vuong test. A real dataset was analyzed and modeled using the specific model selection approaches, and the proper ARMA(1,1) model was selected from the competing ARMA(1,1) models for data fitting. |
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| Keywords: ARMA(1, 1), Cox test, MMLE, tracking interval, Vuong test. |
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Full-Text [PDF 2115 kb]
(601 Downloads)
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Type of Study: Applicable |
Subject:
General
Received: 2021/07/13 | Accepted: 2022/11/10 | Published: 2021/02/19
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