Econometric Methods for Discretely-Sampled Continuous-Time Models

离散采样连续时间模型的计量经济学方法

• 批准号: 0111140
• 负责人: Yacine Ait-Sahalia
• 金额: $ 22.54万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-01 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0111140&HistoricalAwards=false
• 关键词: Econometric; Methods; Discretely; Sampled; Continuous

Interest rates have traditionally been modeled in the economics literature as following continuous-time Markov processes, and more specifically, diffusions. By contrast, recent term structure models often imply non-Markovian continuous-time dynamics. Can discretely sampled interest rate data help decide which continuous-time models are sensible? Within the Markovian world, diffusion processes are characterized by the continuity of their sample paths. It is immediately, obvious that this condition cannot be verified from the observed sample path. By nature, even if the sample path were continuous, the discretely sampled interest rate data will appear as a sequence of discrete change. This grant continues work begun under NSF award 970305 on this fundamental problem in financial economics.This project develops new likelihood-based estimation methods for discretely-sampled continuous-time models and extends our understanding of the properties of estimators in four related situations:1. Since many realistic models in economics involve multiple state variables, the first part of the project develops a closed-form sequence of likelihood functions applicable to arbitrary multivariate diffusion models.2. These functions are used to infer consistent dynamic models from market data.3. Allowing now for jumps, it is shown that the lower the frequency of observation, the more difficult it is to disentangle from discrete data the respective effects of the jump and volatility components. The project makes this intuition rigorous by deriving Fisher's information matrix from an explicit expansion of the likelihood answering questions such as: How fast does the precision of the jump estimates decrease when the frequency of observation decreases? What is the influence on the identifiability of jumps of the relative magnitudes of the (continuous) volatility and (discontinuous) jump parts?4. New issues arise when the data are not only discretely but also possibly randomly spaced in time. The project derives the properties of estimators based on maximum-likelihood with either full or partial information, the generalized method of moments, and discrete sampling schemes such as the Euler approximation. Studying the effect of the sampling randomness, the asymptotic distribution of the various estimators will be decomposed in terms that are due to the discreteness vs. terms due to the randomness of the sampling. This makes it possible to compare the relative costs of ignoring either the discreteness or the randomness of the sampling scheme producing the data. When the estimators are asymptotically biased, their biases will also be analyzed.The project integrates research and education by creating datasets and developing publicly available computer code (both made available through the web, as has been the case for past projects) for each of the main research endeavors funded by this proposal. The results will be disseminated broadly through presentations at seminars, conferences and professional association meetings.

在经济学文献中，利率传统上被建模为遵循连续时间马尔可夫过程，更具体地说，是扩散。相比之下，最近的期限结构模型往往隐含着非马尔科夫连续时间动态。离散抽样的利率数据能否帮助决定哪些连续时间模型是合理的？在马尔可夫世界中，扩散过程的特征是其样本路径的连续性。显而易见的是，这种情况不能从观察到的样本路径中得到验证。从本质上讲，即使样本路径是连续的，离散抽样的利率数据也会以离散变化序列的形式出现。这项研究是970305年度国家自然科学基金奖下关于金融经济学中这一基本问题的工作的继续。本项目为离散抽样的连续时间模型开发了新的基于似然估计的方法，并扩展了我们对四种相关情形下估计量的性质的理解：1.由于经济学中的许多现实模型涉及多个状态变量，本项目的第一部分开发了适用于任意多变量扩散模型的闭合形式的似然函数序列。这些函数用于从市场数据中推断出一致的动态模型。现在考虑跳跃，结果表明，观测频率越低，就越难从离散数据中分离出跳跃和波动分量的各自影响。该项目通过从回答以下问题的可能性的显式展开中推导出费舍尔信息矩阵来使这一直觉变得严格：当观察频率降低时，跳跃估计的精度下降的速度有多快？对(连续的)波动率和(不连续的)跳跃部分的相对幅度的跳跃的可识别性有什么影响？4.当数据不仅是离散的，而且可能在时间上随机分布时，新的问题会出现。该项目基于具有全部或部分信息的最大似然、广义矩方法和离散抽样方案(如欧拉近似)来推导估计器的性质。在研究抽样随机性的影响时，各种估计量的渐近分布将被分解为由于抽样的随机性而导致的离散性对项的项。这使得比较忽略产生数据的抽样方案的离散性或随机性的相对成本成为可能。当估计者有渐近偏差时，他们的偏差也将被分析。该项目通过为该提案资助的每一项主要研究努力创建数据集和开发公开可用的计算机代码(两者都可以通过网络获得，就像过去的项目一样)，将研究和教育结合在一起。结果将通过在研讨会、会议和专业协会会议上的陈述广泛传播。