Research on implementations of computer-intensive selection methods for regularized statistical models

(1)在利用交易债券数据对利率期限结构进行非参数估计时，经验表明，近似远期利率往往会产生更好的结果。然而，这种方法的问题在于，不能合理地使用广义交叉验证来选择正则化参数。在这个项目中，我们建立了一个版本的广义信息准则（GIC），它在确定正则化参数方面具有理论有效性。(2)比较了不同类型的GARCH模型和多元GARCH模型对下行风险的一致性，特别是对风险价值（VaR）的一致性。根据估计的参数进行预测模拟，并通过二项检验将经验超标率与标称尺寸进行比较。我们的结论是动态条件相关模型表现最好，而且它的参数形式简洁。(3)研究了含干预项的未观测分量时间序列模型的估计。数据来自动物给药试验。这些是时间序列数据，比如收缩压，舒张压，心率等等。我们考虑了一个时间序列模型，将观测分解为趋势、平稳自回归部分和指数型干预项，使我们能够通过模型选择来估计急性毒性。(4)以向公众公开研究成果为目标，研究了基于web的时间序列分析软件在线学习系统。

(1) In nonparametric estimation of term structures of interest rates from traded bond data, it is empirically well-known that approximating forward rate often yields better result. The problem of this approach is, however, that the use of generalized cross-validation cannot be justified to choose regularization parameters. In this project, we established a version of generalized information criteria (GIC) that holds theoretical validity in the determination of regularization parameter. (2) We compared the performance of various types of GARCH models and multivariate GARCH models in terms of the coherency of downside risks, especially Value at Risk (VaR). Given the parameters estimated, we performed prediction simulation and compared the empirical exceedance rate with nominal size through a binomial test. Our conclusion is that Dynamic Conditional Correlation model performs best, together with its parsimonious parametric form. (3) Estimation of unobserved components time series models with intervention terms are studied. Data come from animal dose administration testing. These are time series data such as systolic blood pressure, diastolic blood pressure, heart rate and so on. We considered a time series model to decompose observation into trend, stationary autoregressive part and an exponential type intervention term, which enabled us to estimate acute toxicity through model selection. (4) Aiming disclosure of the research results to the public, online learning system on the web based time series analysis software was studied.