Bayesian Model Evaluation and Prediction of Economic Time Series

9422922彼得·菲利普斯模型的选择、模型简化和良好预测模型的确定都是经验计量经济学研究中的重要内容。当时间序列是非平稳的时，模型选择的一个方面是如何对数据的非平稳进行建模(例如，随机趋势与确定性趋势还是趋势突变)。这一选择虽然困难，但对样本外预测和预测置信集的表现有很大影响。此外，在实际的商业和金融研究中，我们有时面临同时对大量序列进行建模或预测的需要。在这种情况下，我们需要模式选择的自动化程序，能够考虑到一系列的关键方面，如它的平稳性或缺乏平稳性。这项研究的三个项目中的第一个是关于开发和证明用于经济时间序列分析的这种程序的合理性。所采用的方法是贝叶斯方法，并建立在模型确定、假设检验和存在非平稳性情况下的预测的思想上，PI在最近的研究中提出了这一点。PI的第二个项目着眼于当误差是非平稳的时候的核回归。虽然核回归理论在平稳时间序列的情况下已经得到了很好的发展，但对于单位根或积分过程的情况似乎还没有理论。在这种情况下，核回归的一个问题是估计器经常是不一致的。这项研究开发了修正的核估计，在存在非平稳性的情况下，无论有没有长记忆，都是一致的。第三个项目是PI关于“完全修正的”VAR(FM-VAR)估计的工作的扩展。这些估计量可以利用序列之间潜在的协整联系，而不必明确它们的形式或维度，也无需进行初步测试。本研究扩展了前人的工作，允许在同一VAR中同时存在I(0)、I(1)和I(2)回归变量。它没有对任何回归变量的协整程度或协整顺序做出任何具体的假设，也没有对协整等级进行预先测试。

9422922 Peter Phillips Model choice, model simplification and the determination of good models for prediction are all important elements in empirical econometric research. When times series are nonstationary, an aspect of model choice is how to model the nonstationarity of the data (e.g., stochastic trends versus deterministic trends versus trend breaks). Although difficult this choice has a substantial impact on the performance of out-of-sample forecasts and forecast confidence sets. Furthermore, in practical business and financial research we are sometimes faced with the need to model or predict large number of series simultaneously. In such situations we need automated procedures for model selection that can take account such critical aspects of a series as its stationarity or lack thereof. The first of the three projects in this research is concerned with the development and justification of such procedures for use in the analysis of economic time series. The methods employed are Bayesian and build on ideas on model determination, hypothesis testing, and forecasting in the presence of non-stationarity that the PI has put forward in recent research. The second project by the PI looks at kernel regression when the errors are nonstationary. Although kernel regression theory is quite well developed in the stationary time series case, there appears to be no theory for case of unit roots or integrated processes. One problem with kernel regression in this case is that estimators are often inconsistent. The research develops modified kernel estimators that are consistent in the presence of nonstationarity both with and without long memory. The third project is an extension of the PIs work on "fully modified" VAR (FM-VAR) estimators. These estimators can take advantage of potential cointegrating links between series without having to be explicit about their form or dimension and without preliminary testing. This research extends the previous work so as to allow for I(0), I(1) , and I(2) regressors simultaneously in the same VAR. It proceeds without making any specific assumptions about the degree of cointegration or the order of cointegration of any of the regressors, and without pretesting of the cointegrating rank.