کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10527206 | 958741 | 2013 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Some limit theorems for Hawkes processes and application to financial statistics
ترجمه فارسی عنوان
بعضی از قضیه های محدود برای پردازش هاوکس و کاربرد آن در آمار مالی است
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
In the context of statistics for random processes, we prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval [0,T] when Tââ. We further exhibit the asymptotic behaviour of the covariation of the increments of the components of a multivariate Hawkes process, when the observations are imposed by a discrete scheme with mesh Î over [0,T] up to some further time shift Ï. The behaviour of this functional depends on the relative size of Î and Ï with respect to T and enables to give a full account of the second-order structure. As an application, we develop our results in the context of financial statistics. We introduced in Bacry et al. (2013) [7] a microscopic stochastic model for the variations of a multivariate financial asset, based on Hawkes processes and that is confined to live on a tick grid. We derive and characterise the exact macroscopic diffusion limit of this model and show in particular its ability to reproduce the important empirical stylised fact such as the Epps effect and the lead-lag effect. Moreover, our approach enables to track these effects across scales in rigorous mathematical terms.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 123, Issue 7, July 2013, Pages 2475-2499
Journal: Stochastic Processes and their Applications - Volume 123, Issue 7, July 2013, Pages 2475-2499
نویسندگان
E. Bacry, S. Delattre, M. Hoffmann, J.F. Muzy,