Non- and Semi-parametric Identification and Prediction of Autoregressive Models, with Applications to Econometrics

(1)非参数和半参数自回归条件异方差(ARCH)模型的数据驱动估计、检验和多步预测，以结合经典ARCH模型的指数衰减特性和非参数灵活性；(2)非参数和半参数季节性自回归模型的估计和滞后选择，提高了半参数模型的效率；(3)高阶相互作用项的检验和线性检验，使模型更简单，更容易解释，并提高估计精度；(4)多变量时间序列和波动率函数的滞后选择，它有助于识别变量之间的简约模型和隐藏结构；(5)加性系数自回归模型和函数系数自回归模型的非参数多步预测。欧元兑美元每日汇率和美国月度失业率等经济指标是重要的金融时间序列。在犯罪研究中，几年来每个月发生的犯罪数量有助于发现犯罪受害者的模式。时间序列分析试图从数据中发现未来的观测与过去的观测之间的关系，通常是通过一些基本函数。然而，最近的研究努力证明了对该系列强加过于简单化的结构的缺点。这项研究开发了灵活的新方法来理解更广泛的一类时间序列数据的动态结构，对于这些数据，观测之间的关系是非线性的、无限相关的和/或季节性的。例如，月度失业率数据通常呈现出最适合用半参数季节性模型描述的季节性模式。这项研究使人们能够更准确地根据过去的信息预测未来的观测结果。改进对外汇、股票和其他波动价格的预测，将提供有关未来经济状况的关键信息。对各种经济指标相互作用的新见解可能导致更知情的经济发展战略。通过本研究开发的工具也具有分析非经济时间序列数据的潜力。例如，对未来犯罪率的季节性预测可能有助于执法机构制定更有效的犯罪预防计划。

This research focuses on (1) data-driven estimation, testing, and multi-step prediction for non- and semi- parametric autoregressive conditional heteroscedastic (ARCH) models, in order to combine the exponentially decaying feature of classic ARCH models with nonparametric flexibility; (2) estimation and lag selection using plug-in bandwidths for non- and semi- parametric seasonal autoregressive models, with improved efficiency for the semiparametric models; (3) test of higher order interaction terms and a linearity test that leads to simpler models with easier interpretation, and improved estimation accuracy; (4) lag selection for multivariate time series and volatility functions, which aids in identifying parsimonious models and hidden structures among variables; and (5) nonparametric multi-step prediction for additive and functional coefficient autoregressive models.A time series consists of numbers observed over time. Economic indicators such as the daily exchange rate of the Euro against the US Dollar and the monthly rate of unemployment in the United States are important financial time series. In the study of crimes, the number of crimes committed each month over several years are useful for finding patterns of crime victimization. Time series analysis attempts to discover from the data how future observations relate to past ones, usually through some elementary functions. Recent research efforts, however, have demonstrated the disadvantages of imposing simplistic structures on the series. This research develops flexible new methods to understand the dynamic structure of a much broader class of time series data for which the relationship among observations are nonlinear, infinitely dependent and/or seasonal. For instance, monthly unemployment rate data usually exhibit seasonal patterns that are best described by a semiparametric seasonal model. This research enables one to predict future observations based on past information much more accurately. Improved forecasting of foreign exchange, stock and other volatile prices will provide crucial information about the future state of the economy. New insights into the interaction of various economic indicators could lead to a more informed strategy of economic development. The tools developed through this research have the potential for analyzing non-economic time series data as well. For instance, seasonal forecasts of future crime rates may help law enforcement agencies to create a more effective crime prevention plan.