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اختبارات التكامل الكسري في نماذج ARIMA == Tests of Fractional Integration In Models ARIMA
Author name:
احلام حنش كاطع
Supervisor name:
لميعة باقر جواد الجواد
General topic:
Administration and Economics
Specific topic:
Statistics
Degree:
Master
University:
University of Baghdad - Faculty Of Administration And Economics - Department Of Statistics
Language:
Arabic
University location:
Baghdad
First pages:
07T3378 - p.pdf
Abstract:
توجد انواع من العمليات العشوائية المستقرة لا نستطيع ان نعدها كنماذج من الاوساط المتحركة او الانحدار الذاتي اذ انها تحتوي عل خصائص هذين النوعين (انحدار ذاتي - اوساط متحركة) فمثل هــذه العمليات تسمـى بالنماذج المختلطة ويرمز لها بـ (ARMA(p, q)) ولكي تتوفر ال | There are many types of stationary stochastic processes that can’t be considered as models of moving average or autoregressive, because they have the characteristics of these two kinds : (Autoregressive - Moving average). These processes are called mixed models and referred to as (ARMA (p, q)). In order that these models have the stability, the roots of equation must equal zero , outside the unit circle and also for the Inevitability, the roots of equation must equal zero , outside the unit circle. These models may be non - stationary in themselves but they will be stationary after many transformations or differences, so the models which explains this process will be different from the original, because it must contain those differences that have been done on the original models. These stationary models are called ARIMA, and the differences may be inter numbers or fractional numbers, then, the differences will be fractional numbers ranged between [0.5 , - 0.5] , and the model is called ARFIMA or what is called as fractional integration, and (d) represents the parameter of the fractional differences. In this study, three methods have been applied to test the non stationary models of the fractional integration (ARFIMA). One of the common test used is that which is based on the periodogram regression suggested by GPH, whereas LO suggests another test modified from the classical test which is known as modified rescaled range (MRR). A third test has been presented which adopts the idea of lagrang multiple which is known as : (LM). These tests have been applied in four models; AR, MA, ARCH and ARFIMA. The way of simulation and building programs using Visual basic (V. B) has been employed the percentages of the times of rejection have been gained out of 1000 frequencies for each method of the test, for each parameter and for more then one sample. The fractional integration parameter of the first test GPH has been compared with table (t), because variance is unknown, as to the second test MRR, the value (R/S) is compared with table LO, the third test LM is compared with table Z.
