Subordinated Stock Price Models: Heavy Tails and Long-Range Dependence in the High-frequency Deutsche Bank Price Record

2000 ◽  
pp. 69-94 ◽  
Author(s):  
Carlo Marinelli ◽  
Svetlozar T. Rachev ◽  
Richard Roll ◽  
Hermann Göppl
Keyword(s):  
Long Range ◽  
High Frequency ◽  
Stock Price ◽  
Heavy Tails ◽  
Long Range Dependence

scholarly journals LONG MEMORY VERSION OF STOCHASTIC VOLATILITY JUMP-DIFFUSION MODEL WITH STOCHASTIC INTENSITY

2020 ◽  
Vol 38 (2) ◽  
Author(s):  
Somayeh Fallah ◽  
Farshid Mehrdoust
Keyword(s):  
Stochastic Volatility ◽  
Long Range ◽  
Diffusion Model ◽  
Long Memory ◽  
Stock Price ◽  
Real Data ◽  
Jump Diffusion ◽  
Heston Model ◽  
Long Range Dependence ◽  
Jump Diffusion Model

It is widely accepted that certain financial data exhibit long range dependence. We consider a fractional stochastic volatility jump diffusion model in which the stock price follows a double exponential jump diffusion process with volatility described by a long memory stochastic process and intensity rate expressed by an ordinary Cox, Ingersoll, and Ross (CIR) process. By calibrating the model with real data, we examine the performance of the model and also, we illustrate the role of long range dependence property by comparing our presented model with the Heston model.

The computation of high frequency S&P 500 long-range dependence volatility using dynamic modified rescaled adjusted range approach

2015 ◽  
Vol 9 ◽  
pp. 5915-5924
Author(s):  
Chin Wen Cheong ◽  
Zaidi Isa ◽  
Tan Pei Pei ◽  
Lee Min Cherng
Keyword(s):  
Long Range ◽  
High Frequency ◽  
Long Range Dependence

scholarly journals How system performance is affected by the interplay of averages in a fluid queue with long range dependence induced by heavy tails

1999 ◽  
Vol 9 (2) ◽  
pp. 352-375 ◽  
Author(s):  
David Heath ◽  
Sidney Resnick ◽  
Gennady Samorodnitsky
Keyword(s):  
Long Range ◽  
System Performance ◽  
Heavy Tails ◽  
Long Range Dependence ◽  
Fluid Queue

scholarly journals Marcinkiewicz law of large numbers for outer products of heavy-tailed, long-range dependent data

2016 ◽  
Vol 48 (2) ◽  
pp. 349-368
Author(s):  
Michael A. Kouritzin ◽  
Samira Sadeghi
Keyword(s):  
Long Range ◽  
Heavy Tails ◽  
Law Of Large Numbers ◽  
Nonlinear Function ◽  
Dependent Data ◽  
Long Range Dependence ◽  
Linear Processes ◽  
Strong Law ◽  
Large Numbers ◽  
Heavy Tailed

Abstract The Marcinkiewicz strong law, limn→∞(1 / n1/p)∑k=1n(Dk - D) = 0 almost surely with p ∈ (1, 2), is studied for outer products Dk = {XkX̅kT}, where {Xk} and {X̅k} are both two-sided (multivariate) linear processes (with coefficient matrices (Cl), (C̅l) and independent and identically distributed zero-mean innovations {Ξ} and {Ξ̅}). Matrix sequences Cl and C ̅l can decay slowly enough (as |l| → ∞) that {Xk,X ̅k} have long-range dependence, while {Dk} can have heavy tails. In particular, the heavy-tail and long-range-dependence phenomena for {Dk} are handled simultaneously and a new decoupling property is proved that shows the convergence rate is determined by the worst of the heavy tails or the long-range dependence, but not the combination. The main result is applied to obtain a Marcinkiewicz strong law of large numbers for stochastic approximation, nonlinear function forms, and autocovariances.

Introduction Non-conventional Queueing Models: Heavy Tails, Long-Range Dependence, and Rare Events

2004 ◽  
Vol 46 (1/2) ◽  
pp. 5-7
Author(s):  
Takis Konstantopoulos ◽  
Stan Zachary ◽  
Serguei Foss
Keyword(s):  
Long Range ◽  
Heavy Tails ◽  
Rare Events ◽  
Long Range Dependence ◽  
Queueing Models
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