Abstract    In this paper, for the first time, the subject of change point estimation has been utilized in the stationary state of auto regressive moving average (ARMA) (1, 1). In the monitoring phase, in case the features of the question pursue a time series, i.e., ARMA(1,1), on the basis of the maximum likelihood technique, an approach will be developed for the estimation of the stationary state’s change point. To estimate unidentified parameters following the change point, the dynamic linear model’s filtering was utilized on the basis of the singular decomposition of values. The proposed model has wide applications in several fields such as finance, stock exchange marks and rapid production. The results of simulation showed the suggested estimator’s effectiveness. In addition, a real example on stock exchange market is offered to delineate the application.

Keywords    Auto Regressive Moving Average Model Change Point Estimation; Dynamic Linear Model; Maximum Likelihood Estimation; Singular Value Decomposition

چکیده    در این مقاله، برای اولین بار، موضوع تخمین نقطه تغییر در حالت مانایی سری زمانی آرما مرتبه اول بکار رفته است. در فاز کنترل، تکنیک حداکثر درستنمایی برای تخمین نقطه تغییر حالت مانایی، توسعه پیدا کرده است. در این مدل به منظور تخمین پارامترهای نامعلوم بعد از نقطه تغییر، از روش فیلترینگ (نوعی از مدل خطی پویا) بر مینای روش تجزیه مقادیر منفرد استفاده شده است. مدل ارایه شده در زمینه¬های زیادی همچون بازار سهام، فاینانس، تولید انبوه و ... کاربرد دارد. نتایج شبیه¬سازی حاکی از کارایی، مدل پیشنهادی است. همچنین یک مثال از کاربرد واقعی مدل پیشنهادی در بازار سهام ارایه شده است.

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