Trends And Empirical Econometric Limits

关系到所有实际经济分析的一个重要问题是，我们可以在多大程度上通过发展理论、观察和拟合模型来理解经济现象。在实践中，一个特别相关的问题是，我们使用通过这种过程获得的经验模型来预测未来的观测结果是否存在限制。寻找极限的定量表达式是该项目的主要主题。经验知识的一个主要限制是，任何给定数据的真实模型是未知的，并且在所有实际情况下都是未知的。这是因为，即使所建立的模型是正确的，它仍然取决于需要从数据中估计的参数。通常，相对于需要估计的参数的数量而言，数据是稀缺的，在具有某些函数表示的模型中尤其如此，这就需要使用非参数或半参数方法。在这种情况下，人们可能会认为，建模的经验限制比有限参数模型更大。使用Jorma Rissanen在1987年率先提出的推理，作者在1999年与Werner Ploberger的合作中表明，经验模型(根据其对数似然比)与真实模型的接近程度存在一个量化界限。这一界限取决于数据本身以及所使用的模型。在对经济数据的应用中，一个似乎很重要的发现是，界限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平稳时的大。这一结果定量地表达了一个直观的观点，即趋势数据比非趋势数据更难预测。该项目发展并将这种类型的限制结果扩展到存在局部和总体规范误差的模型，扩展到参数空间的维度是无限的或可能随着样本大小而增长的非参数情况，即随着更多数据的获得而建模变得更加雄心勃勃的情况。该项目还寻求建立预测误差分歧的显式表示，以便量化经验预测能力的限制。这个项目的目的是将理论发展到一个阶段，在这个阶段，极限将对经验研究人员有用，特别是在实施旨在实现经验边界的模型确定标准的过程中。在与这一主要主题相关的研究的附属分支中，该项目研究了更明确的趋势回归问题，其中趋势的量级没有具体说明，但必须被估计，在数据中存在长期记忆，可能是非平稳的，记忆参数必须以半参数估计，并且存在非平稳的解释数据，但因变量有限。后一项研究与美联储和财政部的市场干预政策相关。因此，货币政策干预是一个二元决策(干预或不干预)，但决定它的解释变量涉及大量经济数据，其中许多数据具有非平稳特征，如工业生产的增长特征和股票价格的随机游荡行为。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，从而导致市场干预。例如，这些概率定律能否解释，市场干预的趋势为何会被定期干预所打破，变成长期的几乎不干预？

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?