Empirical Similarity: estimation, multivariate extensions, and applications

经济学家的目标是用正式的决策规则来描述现实，这些规则假设特定的因果关系，并通过计量经济分析进行经验验证。然而，有时手头没有适当的决策规则，只有一些经验丰富的案例被定义为一系列条件、行为及其结果。那么，基于案例的判决应该类似于那些与当前案例相似的经验案例中的成功判决。经验相似性方法为基于案例的决策提供了计量框架，并假定感兴趣的变量是由当前和以前案例的相似性加权的历史结果的总和。因此，专家系统的权重是时变的，由外部变量非线性确定，从而可以直接从数据中揭示基于案例的决策的原理。它的应用已经在实验经济学、房地产价格建模、预测金融市场波动或评估法律司法决策方面提供了有用的见解。然而，仍然有一些尚未解决的计量经济学问题以及有趣的应用将在这个项目中解决。在项目的理论部分，我们将分析，首先，经验数据的哪些性质适合应用ES技术，以及如果基本假设被违反会发生什么。其次，现有ES模型估计的不稳定性阻碍了其在许多重要问题背景下的应用。我们的目标是提出用于稳定ES估计过程的正则化技术，并提供关于变量选择和降维问题的结果。第三，目前的理论结果主要集中在单变量数据上，而多变量ES(MES)模型用于描述变量向量的决策。我们的目标是开发MES模型，特别关注模型的选择、推断和稳健估计。此外，在项目的实证部分，我们将把ES概念应用到经济和金融问题的研究中。我们计划调查美国联邦储备委员会(Fed)通过调整名义利率实施的货币政策是由正式规则驱动的，还是主要由经验驱动的、基于案例的论点。然后，我们将从ES的角度将技术分析视为资产定价的非参数方法。我们专注于识别价格模式并衡量不同模式之间的相似性，以获得有关未来价格的信息。接下来，我们将考虑各种投资组合选择策略，并通过ES方法确定不同策略的权重。综上所述，该项目将涵盖一系列理论问题和潜在的应用，ES方法是基于案例的决策的计量经济学设置，与基于规则的正式建模相比。

Economists aim to describe reality with formal decision rules which postulate specific causal relationships validated empirically by econometric analysis. However, sometimes there is no appropriate decision rule at hand, but only some experienced cases defined as a set of conditions, acts and their outcomes. Then a case-based decision should resemble successful decisions in those experienced cases which are similar to the current case. The empirical similarity (ES) approach provides econometric framework for case-based decisions and presumes that the variable of interest is a sum of historical outcomes weighted by similarities of current and previous cases. Hence, the ES weights are time-varying and determined by nonlinearly by exogenous variables which allows to reveal the principles of case-based decision making directly from the data. Its application has already provided useful insights in experimental economics, modeling real estate prices, predicting volatilities on financial markets or evaluating legal juridical decisions. However, there are still some unresolved econometric issues as well as interesting applications which we will address in this project.In the theoretical part of the project we are going to analyse, first, which properties of empirical data are suitable for applying ES technique and what happens if the underlying assumptions are violated. Second, estimation instability of existing ES models hinders their application in many important problem settings. Our objective is to propose regularization techniques for stabilizing ES estimation procedure as well as to provide results about variable selection and dimension reduction issues. Third, the current theoretical results focus on univariate data whereas multivariate ES (MES) models are required for decisions characterized by vectors of variables. We aim to develop MES models with a particular attention paid to model selection, inferences and robust estimation.Further, in the empirical part of the project we are going to apply the ES concept to research problems in economics and finance. We plan to investigate whether monetary policy of the US Federal reserve implemented by adjustments of the nominal interest rate is driven by formal rules or primarily by experience relying on case-based arguments. Then, we are going to consider technical analysis as a nonparametric approach to asset pricing from the ES perspective. We focus on recognition of price patterns and measuring similarities between different patterns in order to get information about future prices. Next, we will consider various portfolio selection strategies and determine the weights of different strategy by means of ES approach.Summarizing, the project will cover a set of theoretical problems and potential applications of the promising ES approach which is the econometric setting for case-based decisions contrasted to formal rule-based modeling.