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العنوان
Statistical Analysis of Stable Discrete Time Series Using Missed Observations and Its Applications /
الناشر
MOHAMED ALI SHAPPAN ALARGT,
المؤلف
ALARGT, MOHAMED ALI SHAPPAN.
هيئة الاعداد
باحث / MOHAMED ALI SHAPPAN ALARGT
مشرف / Mohamed Abou El-Fotouh Ghazal
مشرف / Amira Ibrahim Al-Desouki
مناقش / Mahmoud Taha Yassin
الموضوع
التحليل الاحصائي. الاحصاء التحليلي.
تاريخ النشر
2019.
عدد الصفحات
149 p. :
اللغة
الإنجليزية
الدرجة
الدكتوراه
التخصص
الإحصاء والاحتمالات
تاريخ الإجازة
1/6/2019
مكان الإجازة
جامعة دمياط - كلية العلوم - Mathematics
الفهرس
Only 14 pages are availabe for public view

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Abstract

The main objective of this work is to develop methods of computation and research of statistical analysis of discrete time series by using missing values and Bernoulli sequence. Time series analysis is an important aspect of statistical studies that are closely linked to natural sciences. The time series spectral study is one of the important trends in this field, which plays an important role in understanding the behavior of the time series based on the values of the series. Slutsky [63], was the first to use the Periodogram as an estimate of the density spectral function of stable processes, providing many of the statistical properties of this estimate, which is highly dependent on the Fourier Transform. Brillinger and Ghazal et al studied asymptotic properties of the finite Fourier transform in the case where all observations are available. Ghazal, Mokaddis and El-Desokey [37], studied asymptotic properties of the expanded finite Fourier transform in the case where there are some randomly missing observations for , vector-valued series by using data window and Bernoulli sequence. We have developed these studies to include the case where there are some randomly missing observations for vector-valued time series { , vector-valued series and , vector-valued series}. In chapter I, we described some definitions of time series and used of analytical spectrum of time series and provide the reader with the basic terminology of the thesis, fundamental concepts and theorems that form the basic of time series analysis and spectral density estimate. In chapter II, we determined the asymptotic Properties Of estimates the desired , ,we constructed the expanded finite Fourier transform for a zero mean vector-valued strictly stability discrete series with missed observations using data window, and we found their asymptotic distribution. In chapter III, we considered the asymptotically properties of second-order statistics based on sample values from an vector-valued time series. We considered the case where observations are missed in some more general way, One way to simplify it is assuming that , vector-valued strictly stability time series where , represents the studied series and , represents the studied series after being filtered . Our method of proceeding is to derive a general theorem on the asymptotic behavior of the periodogram, including a necessary uniform error term. In fact the periodograms are based on the discrete Fourier transform of the sample. Brillinger [11], indicated the elementary asymptotic sampling properties of this transform. In addition, the pleasant analytic properties of Fourier transform are well known. We have therefore been led to take the periodogram as the basis of our work. We prove that distinct values of the periodogram tend to be asymptotically independent and have Wishart distributions. The primary focus was on defining the modified series and study the statistical properties of finite Fourier transform of underling process. The observed series included some randomly missing observations is defined and some conditions assumed. The statistical properties of the modified series, , are discussed. We defined the finite Fourier transform and the statistical properties of the finite Fourier transform for modified series are studied. We suggested a consideration of the matrix of second-order modified periodogram and the asymptotic properties are investigated. We constructed asymptotically unbiased and consistent estimate of the matrix of second-order spectral measures. Also, The statistical properties of the matrix of spectral densities are discussed. We prove that the matrix of spectral densities is asymptotically unbiased and consistent estimate of the matrix of second-order of average spectral densities. In this thesis, we have studied some cases as a practical application and have published their results in the form of two papers in an international journal.