英文标题：
《Chaos in Fractionally Integrated Generalized Autoregressive Conditional
Heteroskedastic Processes》
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作者：
Adil Yilmaz, Gazanfer Unal
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最新提交年份：
2016
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英文摘要：
Fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) arises in modeling of financial time series. FIGARCH is essentially governed by a system of nonlinear stochastic difference equations ${u_t}$ = ${z_t}$ $(1-\\sum\\limits_{j=1}^q \\beta_j L^j)\\sigma_{t}^2 = \\omega+(1-\\sum\\limits_{j=1}^q \\beta_j L^j - (\\sum\\limits_{k=1}^p \\varphi_k L^k) (1-L)^d) u_t^2$, where $\\omega\\in$ R, and $\\beta_j\\in$ R are constant parameters, $\\{u_t\\}_{{t\\in}^+}$ and $\\{\\sigma_t\\}_{{t\\in}^+}$ are the discrete time real valued stochastic processes which represent FIGARCH (p,d,q) and stochastic volatility, respectively. Moreover, L is the backward shift operator, i.e. $L^d u_t \\equiv u_{t-d}$ (d is the fractional differencing parameter 0$<$d$<$1). In this work, we have studied the chaoticity properties of FIGARCH (p,d,q) processes by computing mutual information, correlation dimensions, FNNs (False Nearest Neighbour), the Lyapunov exponents, and for both the stochastic difference equation given above and for the financial time series. We have observed that maximal Lyapunov exponents are negative, therefore, it can be suggested that FIGARCH (p,d,q) is not deterministic chaotic process.
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中文摘要：
分数积分广义自回归条件异方差（FIGARCH）出现在金融时间序列建模中。FIGARCH基本上由非线性随机差分方程组${u_t}$=${z_t}$$（1-\\sum\\limits{uj=1}^q\\beta_j L^j）\\sigma_{t}^2=\\omega+（1-\\sum\\limits{j=1}^q\\beta_j^j-（\\sum\\limits{k=1}^p\\varphi k{k L^k^k）（1-L）^d）u__{t^2，其中，β和ωR$j参数是常数，$\\{u\\u t\\}{t\\in}^+}$和$\\{sigma\\u t\\}{{t\\in}^+}$是离散时间实值随机过程，分别代表FIGARCH（p，d，q）和随机波动率。此外，L是后移运算符，即$L^d u_t\\equiv u_{t-d}$（d是分数差分参数0$<$d$<$1）。在这项工作中，我们通过计算互信息、关联维数、FNN（假最近邻）、Lyapunov指数，以及上述随机差分方程和金融时间序列，研究了FIGARCH（p，d，q）过程的混沌性。我们观察到最大Lyapunov指数为负，因此，可以认为FIGARCH（p，d，q）不是确定性混沌过程。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics 数学
二级分类：Dynamical Systems 动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Statistics 统计学
二级分类：Other Statistics 其他统计数字
分类描述：Work in statistics that does not fit into the other stat classifications
从事不适合其他统计分类的统计工作
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