Inference for Stochastic Processes and Applications

我的研究计划的长期目标是开发新的方法和模型来研究随机过程的推理。本文的工作涉及随机过程，如非线性时间序列模型、最近提出的随机系数计数时间序列模型、循环计数时间序列模型、波动率模型、无穷方差随机过程和半鞅。贝叶斯系统和非贝叶斯系统中的正则化组合估计函数理论的统一方法将在离散时间模型和半鞅的背景下使用，以获得正则化的滤波算法。对于具有时变方差-协方差矩阵的网络，正则滤波在动态数据科学中也是有用的。 (A)正规化的时间序列方法使数据科学家和风险管理人员能够增强模型的预测能力，并改善风险预测的质量。 虽然正则化估计已被证明在许多应用中表现良好，但它们在获得金融风险预测/过滤器方面的用途尚未被研究。正规化 对波动率和风险价值的数据驱动的自适应预测算法将进行详细研究，并将应用于自动化交易系统。在本提案中，使用了一种估计 将研究函数方法、随机系数时间序列模型、状态空间模型、随机波动模型和半鞅的正则化滤波。 (B)人们对具有无穷方差的随机过程越来越感兴趣。例如，Fama(2013年诺贝尔计量经济学模型奖获得者)研究了估计 以及对无限方差回归模型的预测。对于具有无穷方差稳定误差的时间序列模型，密度的闭合表达式不可用，因此不容易获得最大似然估计。我们使用了组合的正弦和余弦估计函数来研究估计。我开发了一种最大信息递归估计方法，并将其应用于金融数据。在这项建议中，我将研究使用正弦和余弦估计函数的无限方差模型的最大信息过滤估计。 (C)在今后的工作中，我将研究基于联合估计函数的无偏估计。我将把所提出的方法应用到数据驱动的投资组合优化和网络推理的研究中。 拟议的研究将为培训各级高素质人员提供机会。他们将学习正则化过滤、正则化风险预测和最优投资组合选择中的统计理论和算法/R编码。正则化预测和正则化过滤器将为金融、计算机科学和农业经济学的应用研究人员提供实用工具。

The long-term goal of my research program is to develop novel methods and models to study inference for stochastic processes. The work proposed here involves stochastic processes such as nonlinear time series models, recently proposed random coefficient count time series models, circular count time series models, volatility models, infinite variance stochastic processes and semimartingales. The unified method of regularized combined estimating function theory in a Bayesian set-up as well as in a non-Bayesian set-up will be used in the context of discrete time models and semimartingales to obtain regularized filtering algorithms. Regularized filtering is also useful in dynamic data science for networks with time varying variance-covariance matrix. (a) Regularized time series methods allow data scientists and risk managers to enhance the forecasting power of a model and to improve the quality of the risk forecasts. While regularized estimates have been shown to perform well in many applications, their use in obtaining financial risk forecasts/filters has not yet been studied. Regularized data-driven adaptive forecasting algorithms for volatility and value at risk will be studied in detail and will be applied in automated trading systems. In this proposal, using an estimating function approach, regularized filtering for random coefficient time series models, state space models, stochastic volatility models and semimartingales will be studied. (b) There has been a growing interest in stochastic processes with infinite variance. For example Fama (2013 Nobel Prize winner for econometric modelling) studied estimation and prediction for infinite variance regression models. For time series models with infinite variance stable errors, closed form expressions for the density are not available and hence the maximum likelihood estimate cannot readily be obtained. We have used combined sine and cosine estimating functions to study estimation. I have developed a maximum information recursive estimation method and applied it to financial data. In this proposal, I will study maximum information filtered estimates for infinite variance models using sine and cosine estimating functions. (c) In further work, I will investigate de-biased estimates based on combined estimating functions. I will apply the proposed methodology to the study of data driven portfolio optimization and network inference. The proposed research will provide opportunities for training of highly qualified personnel at all levels. They will learn statistical theories and algorithms/R coding in regularized filtering, regularized risk forecasting and optimal portfolio selection. The regularized forecasts and regularized filters will provide practical tools to applied researchers in finance, computer science and AgriEconomics.