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摘要翻译：
我们提出了一族模型，使预测估计时变极端事件概率的重尾和非线性依赖的时间序列。模型是一个具有条件log-Laplace随机波动的白噪声过程。与其他类似的随机波动性形式化相比，该过程的条件概率结构具有解析表达式，能够直接估计动态变化的极端事件概率。过程和波动率是条件帕累托尾的，其尾指数由对数波动率的平均绝对新息的倒数给出。这种形式可以适应各种各样的非线性依赖，以及条件幂律尾行为，从弱非高斯尾到类柯西尾。我们提供了一个计算简单的估计过程，它使用过程的动态大偏差概率的渐近逼近。我们通过仿真研究证明了估计量的有效性。然后，我们展示了该方法对波动率由混沌Lorenz系统驱动的模拟非线性时间序列的预测能力。最后，我们给出了一个实证应用，结果表明，这种简单的建模方法可以有效地用于金融时间序列的动态预测尾部推断。
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英文标题：
《Dynamic tail inference with log-Laplace volatility》
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作者：
Gordon V. Chavez
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最新提交年份：
2019
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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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：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace stochastic volatility. In contrast to other, similar stochastic volatility formalisms, this process has analytic expressions for its conditional probabilistic structure that enable straightforward estimation of dynamically changing extreme event probabilities. The process and volatility are conditionally Pareto-tailed, with tail exponent given by the reciprocal of the log-volatility's mean absolute innovation. This formalism can accommodate a wide variety of nonlinear dependence, as well as conditional power law-tail behavior ranging from weakly non-Gaussian to Cauchy-like tails. We provide a computationally straightforward estimation procedure that uses an asymptotic approximation of the process' dynamic large deviation probabilities. We demonstrate the estimator's utility with a simulation study. We then show the method's predictive capabilities on a simulated nonlinear time series where the volatility is driven by the chaotic Lorenz system. Lastly we provide an empirical application, which shows that this simple modeling method can be effectively used for dynamic and predictive tail inference in financial time series.
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PDF链接：
https://arxiv.org/pdf/1901.02419
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