Applied Probability and Time Series Modelling

应用概率和时间序列建模

• 批准号: 9972015
• 负责人: Peter Brockwell
• 金额: $ 21.6万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9972015&HistoricalAwards=false
• 关键词: Applied; Probability; Time; Series; Modelling

9972015This research deals with problems in time series analysis related to the theory and application of non-linear models in both discrete and continuous time and to models for integer-valued data. It is concerned with the development of such models, the study of their properties and the investigation of systematic techniques for fitting them to data. Also considered are the large-sample properties of the estimated model parameters and the performance of model-based forecasts. Many of the standard tools of linear time series analysis (e.g. the sample autocovariance function) have substantially different properties when the underlying process is nonlinear and this must be taken into account when they are used in conjunction with nonlinear models. Nonlinear continuous time ARMA models have been found useful in the modeling of financial data. Efficient estimation for these processes and for non-Gaussian and multivariate extensions of these are to be investigated to allow for the observed heavy-tailed behavior of financial time series and to permit the study of the dependence between related financial time series. An alternative promising approach to the analysis of financial time series is to use all-pass linear filters driven by non-Gaussian noise as a possible alternative to the use of nonlinear models. Integer-valued time series are of wide occurrence, for example the weekly numbers of accidents or diagnosed cases of some disease. As for the models considered above, the objective is to develop a systematic approach to the modelling and forecasting of such data.In the last ten years there has been a steadily increasing realization that non-linear time series models provide much better representations of many empirically observed time series than the classical linear models. Many of the properties of non-linear models are however not yet understood and there is a need for the development of new models accompanied by efficient model-fitting procedures. At the same time there has been a surge of interest in continuous-time time series models, partly as a result of the very successful application of stochastic differential equation models to problems in finance, exemplified by the derivation of the Black-Scholes option-pricing formula and its generalizations. This proposal is concerned with the development of non-linear models in both discrete and continuous time with particular emphasis on the application of these models to the representation and forecasting of financial data. Another class of time series which arises frequently in applications and for which systematic analysis is relatively undeveloped are those in which the observations are integer-valued. For these series also a systematic approach to model-building and forecasting is proposed.

9972015本研究涉及时间序列分析中离散时间和连续时间非线性模型的理论和应用以及整数值数据模型的问题。它关注的是这些模型的发展，它们的性质的研究和系统的技术，以适应数据的调查。还考虑了估计模型参数的大样本特性和基于模型的预测的性能。线性时间序列分析的许多标准工具（例如样本自协方差函数）在潜在过程是非线性时具有本质上不同的性质，当它们与非线性模型结合使用时必须考虑到这一点。非线性连续时间ARMA模型在金融数据建模中非常有用。对这些过程的有效估计以及对这些过程的非高斯和多元扩展进行研究，以允许观察到金融时间序列的重尾行为，并允许研究相关金融时间序列之间的依赖性。金融时间序列分析的另一种有前途的方法是使用由非高斯噪声驱动的全通线性滤波器作为使用非线性模型的可能替代方法。整数值时间序列的出现范围很广，例如每周的事故数或某种疾病的诊断病例数。至于上面所考虑的模型，其目标是发展一种系统的方法来模拟和预测这些数据。在过去的十年中，人们逐渐认识到非线性时间序列模型比经典线性模型能更好地表示许多经验观测到的时间序列。然而，非线性模型的许多性质尚未被理解，因此需要开发新的模型，并伴随有效的模型拟合程序。与此同时，人们对连续时间序列模型的兴趣激增，部分原因是随机微分方程模型非常成功地应用于金融问题，布莱克-斯科尔斯期权定价公式的推导及其推广就是一个例子。这一建议涉及到在离散和连续时间的非线性模型的发展，特别强调这些模型在金融数据的表示和预测中的应用。在应用中经常出现的另一类时间序列，其系统分析相对不发达，是那些观测值为整数值的时间序列。对于这些系列，还提出了一种系统的模型建立和预测方法。