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مقارنة دوال كثافة الطيف للسلاسل الزمنية غير المستقرة لحجوم عينات غير متساوية مع تطبيق عملي == Comparing Spectral Densities of Non - Stationary of Time Series With Unequal Sample Sizes
Author name:
احلام حنش كاطع
Supervisor name:
لميعة باقر جواد الجواد
General topic:
Administration and Economics
Specific topic:
Statistics
Degree:
Doctorate
University:
University of Baghdad - Faculty Of Administration And Economics - Department Of Statistics
Language:
Arabic
University location:
Baghdad
First pages:
07T3379 - p.pdf
Abstract:
في هذه الاطروحة تم تقدير المسافة بين اي دالتي كثافة طيف لسلسلتين زمنيتين غير متساويتين في الطول مع ادخال عامل الزمن والتردد ومن ثم اختبار التشابه والاختلاف وفق الاختبار الاحصائي (Nievau - ?) من خلال المقارنة بين دوال كثافة الطيف لسلاسل زمنية شبه مستقرة ال | In this thesis the distance between any two spectrum density functions not equals in the length estimated with interring time and frequency factor then testing the similarity and difference according to statistical test (Nievau - ?) through the comparison among spectrum density functions for non - stationary time series and have a diffirent length (sizes). There are many methods for estimating spectral density functions for non - stationary time series, Therefore we study three different methods which are an important methods where every method holds more characteristics of spectral density functions which are : Evolutionary spectrum method, Wigner - Ville spectrum method and Short - time periodogram method. A forth method suggested depends on shrinkage principle called Shrinkage method which is combines the characteristics of these methods and with a deferent weights p_(1 ,) p_2 where the mathematical derivation for computing weights to the past methods and finding the best weights that gives the smallest MSE has been done.Then a comparison among these four methods to select the best method for applicant it in Oral part using (MAPE)criteria. A simulation experiment conducted on a semi - stationary time series which is a special case of non - stationary time series that follows elated process with the from : x(t)=c(t)x_t^0 Where : C(t) is a function depends on t only, x(t) is a stationary time series follows ARMA(p,q) models with different parameters and different sample size, The result of simulation shows that suggested method (shrinkage method) for spectral density is the best in all of models and sample sizetherefore the best method in estimation is used in oral part to estimating the spectral density concentration of airborne particles (TSP) of three stations (Jaderyah, Andalus, Al - Alawi ) in Baghdad province contains the interval ( 2005 - 2011) measured monthly and this series are different in length, the distance between any tow series are estimated then tested The result show that there are no convergence between density function for the spectrums of these three series that’s mean there are a different in air pollution for the three regions according to its nature
