کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10527307 | 958801 | 2016 | 32 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Hawkes and INAR(â) processes
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this paper, we discuss integer-valued autoregressive time series (INAR), Hawkes point processes, and their interrelationship. Besides presenting structural analogies, we derive a convergence theorem. More specifically, we generalize the well-known INAR(p), pâN, time series model to a corresponding model of infinite order: the INAR(â) model. We establish existence, uniqueness, finiteness of moments, and give formulas for the autocovariance function as well as for the joint moment-generating function. Furthermore, we derive a branching-process-as well as an AR(â)-and an MA(â) representation for the model. We compare Hawkes process properties with their INAR(â) counterparts. Given a Hawkes process N, in the main theorem of the paper we construct an INAR(â)-based family of point processes and prove its convergence to N. This connection between INAR and Hawkes models will be relevant in applications.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 126, Issue 8, August 2016, Pages 2494-2525
Journal: Stochastic Processes and their Applications - Volume 126, Issue 8, August 2016, Pages 2494-2525
نویسندگان
Matthias Kirchner,