الفهرس 
AcknowledgmentOnly 14 pages are availabe for public view
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Abstract
The integer valued time series has emerged as an important area of research in many fields such as medicine, insurance, finance, economics and communication. Most of the models of integer valued time series arises are linear. The most common model is the integer valued autoregressive of order one (INAR(1)) with different marginal distributions. In this thesis, we calculate the higher order joint moments, cumulants up to order three, spectrum, bispectrum and normalized bispectrum and we use the normalized bispectrum for checking the linearity of the model. In Chapter 1, we present some fundamental concepts of time series, linear time series models, autoregressive models (AR), moving average models (MA), the autoregressive moving average (ARMA). Some integer valued time series models based on binomial thinning and other operators are given. Also, some statistical propreties of some INAR(1) are stated. In Chapter 2, the higher order joint moments and cumulants are given. The spectrum, bispectrum and normalized bispectrum are stated. Moreover, we present the estimation of spectrum and bispectrum using smoothed periodogram and some lag windows are mentioned. In the next chapters (from 3 to 7), the higher order joint moments, cumulants up to order three, spectrum, bispectrum and normalized bispectrum of the shifted geometric INAR(1) type-II (SGINAR(1)-II), the dependent counting geometric INAR(1) (DCGINAR(1)), the mixed thinning geometric INAR(1) (MTGINAR(1)), the new skew INAR(1) (NSINAR(1)) and the generalized new geometric INAR(1) (- NGINAR(1)) are calculated. The spectrum, bispectrum and normalized bispectrum are estimated using the smoothed periodogram. The bispectrum and normalized bispectrum are used for checking the linearity of these models. Moreover, the higher order joint moments, cumulants , spectrum, bispectrum and normalized bispectrum of the geometric INAR(1) are concluded as a special case of DCGINAR(1) and MTGINAR(1). The higher order joint moments, cumulants , spectrum, bispectrum and normalized bispectrum of the new geometric INAR(1) are concluded as a special case of NSINAR(1), MTGINAR(1) and -NGINAR(1).