Trends And Empirical Econometric Limits

与所有实际经济分析有关的一个重要问题是，通过发展理论、进行观察和拟合模型的过程，我们能够在多大程度上理解经济现象。在实践中，一个特别相关的问题是，是否有限制，我们可以预测未来的观测结果，通过使用这样的过程获得的模型。该项目的主要课题是为这些限制找到定量的表达方式。经验知识的一个主要限制是，任何给定数据的真实模型都是未知的，而且在所有实际情况下都是不可知的。这是因为即使公式化的模型是正确的，它仍然依赖于需要从数据中估计的参数.通常，相对于需要估计的参数数量，数据是稀缺的，尤其是在具有一些函数表示的模型中，需要使用非参数或半参数方法。在这种情况下，人们可能会期望，经验的限制建模大于在有限参数模型。使用Jorma Rissanen在1987年开创的推理，作者在1999年与Werner Ploberger的合作工作中表明，经验模型与真实模型的接近程度（就其对数似然比而言）存在定量界限。这个界限取决于数据本身以及所使用的模型。在经济数据的应用中，一个重要的发现是，边界的大小取决于数据中趋势的存在和性质。特别是，趋势数据的可实现距离比数据静止时更大。这一结果定量地表达了一个直观的概念，即趋势数据比不趋势的数据更难预测。该项目开发并扩展了这种类型的限制结果的模型，有当地和groserrors的规格，非参数的情况下，parametersspace的尺寸是无限的，或者它可能会随着样本量的增长，也就是说，在whereremodeling变得更加雄心勃勃的情况下，更多的数据变得可用。该项目还寻求发展预测误差发散的明确表示，以便量化经验预测能力的限制。本项目的目的是将理论发展到一个阶段，在这个阶段，极限将对实证研究者有用，特别是在实施旨在超越实证界限的模型确定标准方面。在与这一主题相关的研究的附属分支中，该项目研究了趋势回归的更明确的问题，其中趋势的数量级没有指定，但必须估计，当数据中存在长记忆且可能是非平稳的且记忆参数必须半参数估计时，以及当存在非平稳的解释数据但因变量有限时，后一项研究与联邦和财政部的市场干预政策有关。因此，货币政策干预是一个二元决策（干预或不干预），然而决定它的解释变量涉及大量经济数据，其中许多具有非平稳特征，如工业生产的增长特征和股票价格的随机徘徊行为。我们试图了解解释性数据中的各种特征如何转化为二元变量的概率定律，从而进行市场干预。例如，这些概率定律能否解释市场干预的趋势，即长期的小干预被定期干预所打破？

An important issue that bears on all practical economic analysis is the extent to whichwe can expect to understand economic phenomena by the process of developing a theory,taking observations and fitting a model. An especially relevant question in practice iswhether there are limits on how well we can predict future observations using empiricalmodels that are obtained by such processes. Finding quantitative expression for theselimits is the main subject of the project.A primary limitation on empirical knowledge is that the true model for any given datais unknown and, in all practical cases, unknowable. This is because even if the formulatedmodel were correct it would still depend on parameters that need to be estimated fromdata. Often, the data is scarce relative to the number of parameters that need to beestimated, and this is especially so in models that have some functional representationthat necessitates the use of nonparametric or semiparametric methods. In such situationsone might expect that the empirical limitations on modeling are greater than in finiteparameter models. Using reasoning that was pioneered by Jorma Rissanen in 1987, theauthor has shown in collaborative work with Werner Ploberger in 1999 that there is aquantitative bound on how close an empirical model can get (in terms of its log likelihoodratio) to the true model. This bound depends on the data itself as well as the model thatis being used. A discovery that seems important in applications to economic data is thatthe magnitude of the bound depends on the presence and nature of trends in the data.In particular, the achievable distance is greater for trending data than when the data arestationary. This result gives quantitative expresssion to the intuitively appealing notionthat trending data is harder to predict than data that does not trend. The project developsand extends limitation results of this type to models where there are local and grosserrors of specification, to nonparametric situations where the dimension of the parameterspace is infinite or where it may grow with the sample size, that is, in situations wheremodeling becomes more ambitious as more data becomes available. The project also seeksto develop explicit representations of the forecast error divergence so that the limits onempirical forecasting capability are quantifed. The intent of this project is to developthe theory to a stage where the limits will be useful to empirical researchers, especially interms of the implementation of model determination criteria that are designed to achievethe empirical bounds.In subsidiary wings of research that relate to this main theme, the project studiesmore explicit issues of trend regression, where the order of magnitude of the trend isnot specifed but has to be estimated, where there is long memory in the data which ispossibly nonstationary and the memory parameter must be estimated semiparametrically,and where there is nonstationary explanatory data but a limited dependent variable.The latter study is relevant to market intervention policy by the Federal Reserve andTreasury. Thus, monetary policy intervention is a binary decision (intervene or not), yetthe explanatory variables that determine it involve a host of economic data, much of whichhas nonstationary features, like the growth characteristics of industrial production and therandom wandering behavior of stock prices. We seek to learn how various characteristics inthe explanatory data translate into the probability law for the binary variable and, hence,market intervention. Can these probability laws explain, for instance, the tendency ofmarket intervention to lapse into long periods of little intervention broken by periods ofregular intervention?