کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5103461 1480105 2017 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Fractional Brownian motion time-changed by gamma and inverse gamma process
ترجمه فارسی عنوان
زمان حرکت مکعبی برونیا توسط گاما و روند گاما معکوس تغییر می کند
کلمات کلیدی
وابستگی، فرایند گاما، فرآیند گام معکوس، شبیه سازی، برآورد کردن،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
چکیده انگلیسی
Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian. Therefore there is need to consider new classes of systems to model these kinds of empirical behavior. Motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena. Both of them are constructed as the superposition of fractional Brownian motion (FBM) and other process. In the first case the internal process, which plays role of the time, is the gamma process while in the second case the internal process is its inverse. We present in detail their main properties paying main attention to the long range dependence property. Moreover, we show how to simulate these processes and estimate their parameters. We propose to use a novel method based on rescaled modified cumulative distribution function for estimation of parameters of the second considered process. This method is very useful in description of rounded data, like waiting times of subordinated processes delayed by inverse subordinators. By using the Monte Carlo method we show the effectiveness of proposed estimation procedures. Finally, we present the applications of proposed models to real time series.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica A: Statistical Mechanics and its Applications - Volume 468, 15 February 2017, Pages 648-667
نویسندگان
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