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Abstract  

Aggregated processes appear in many areas of statistics, natural sciences and economics and studying their behavior has a considerable importance from a purely probabilistic point of view as well. Granger (1980) showed that aggregating processes of simple structure can lead to processes with much more complex dynamics, in particular, aggregating random coefficient AR(1) processes can result in long memory processes. This opens a new way to analyze complex processes by constructing such processes from simple ‘building blocks’ via aggregation. The basic statistical problem of aggregation theory is, given a sample {Y 1 (N), …, Y n (N)} of size n of the N-fold aggregated process, to draw conclusions for the structure of the constituting processes (“disaggregation”) and use this for describing the asymptotic behavior of the aggregated process. Probabilistically, this requires determining the limit distribution of nonlinear functionals of {Y 1 (N), …, Y n (N)}, which depends sensitively on the relative order of n and N. In this survey paper, we give a detailed asymptotic study of aggregated linear processes with an arbitrary (possibly infinite) number of parameters and apply the results to the disaggregation problem of AR(1) and AR(2) processes. We also discuss the problem of long memory of aggregated processes.

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Acta Veterinaria Hungarica
Authors: Yonca B. Kabak, Mahmut Sozmen, Alparslan K. Devrim, Mert Sudagidan, Funda Yildirim, Tolga Guvenc, Murat Yarim, Yavuz M. Gulbahar, Ishtiaq Ahmed, Efe Karaca and Sinem Inal

significant difference ( P = 0.028; Table 7 ). On the other hand, VEGF gene expression, compared to other genes, was significantly upregulated in both the FSCC from the oral region and in those from the ear, eyelid and nose (fold change: 64.4 and 60.02

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.8 (corresponds to “good”), if the publication places in the AIR range of 60–80; 0.6 (“acceptable”), if the publication places in AIR range 40–60; 0.2 (“fair”), if the publication has an AIR value below 40. With these criteria, an average value of rating

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.72 Finance 30,196 60 0.2 Management 21,645 1,067 4

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