Inference in Heteroscedastic Nonlinear Time Series Under Long Memory With Applications to Finance

项目摘要：在物理科学、经济学和金融学中，离散时间序列的许多实现表现出长记忆，即当滞后趋近于无穷大时，它们作为滞后函数的自协方差以双曲速率降至零。这种过程在原点具有无界的谱密度。本建议的一部分涉及在半参数设置下，为存在回归或解释性协变量的异方差、非光滑、非线性时间序列模型开发渐近最优和稳健估计器，这些模型可能具有长记忆。特别是，计划在这些模型中存在长记忆解释变量以及误差分布未知的情况下，获得由非光滑自回归模型产生的实验的极限。在第二部分中，PI/Co-PI提出了渐近无分布检验，用于拟合参数自回归均值和/或分位数函数到异方差平稳遍历时间序列。这些测试预计是部分和过程的某些鞅变换的函数，不涉及非参数曲线估计。PI/Co-PI还计划与一些现有测试进行比较研究。所得的结果将用于估计感兴趣的参数和检验与金融经济学问题有关的理论。如果远距离观测之间的关联随着观测之间距离的增加而缓慢衰减但持续存在，则称该数据集具有长记忆。在一段时间内观察到的数据集称为时间序列。异方差时间序列是指在给定过去的情况下，当前时间观测值的条件变率取决于过去。这类数据经常出现在经济、金融和物理科学领域。特别地，长记忆异方差时间序列的一个重要例子是现货收益的波动过程。众所周知，这种波动性随着银行对外汇市场的干预而增加。这种干预过程是高度非平滑的时间序列，因为它在大多数时间为零，在某些时间内具有某些爆发。该建议的部分重点是在一类非光滑非线性异方差时间序列模型中开发最佳推理程序。另一部分强调将所得结果应用于开发新的市场效率测试和金融经济学中随时间变化的风险溢价估计，以及提案中提到的有关德国马克和瑞士法郎与美元汇率和商品价格的高频数据。

PROJECT ABSTRACT:In physical sciences, economics, and finance many realizations of discrete time series exhibit long memory, i.e., their autocovariances as a function of lag decrease to zero at a hyperbolic rate as the lag approaches to infinity. Such processes have unbounded spectral densities at the origin. A part of this proposal is concerned with developing asymptotically optimal and robust estimators for heteroscedastic, non-smooth, non-linear time series models in the presence of regression or explanatory covariates that may have long memory, in a semi-parametric setting. In particular, it is planned to obtain the limits of the experiments generated by the non-smooth autoregressive models when there are long memory explanatory variables present in these models and when the error distributions are unknown. In the second part, the PI/Co-PI propose to develop asymptotically distribution free tests for fitting a parametric autoregressive mean and/or quantile function to a heteroscedastic stationary ergodic time series. These tests are expected to be functions of certain martingale transforms of a partial sum processes that do notinvolve nonparametric curve estimation. PI/Co-PI also plan to carry out a comparative study with some of the existing tests. The results obtained will be used to estimate parameters of interest and test theories relevant to problems in financial economics.A data set is said to have long memory if an association between distant observations is slowly decaying but persistent, as the distance between observations increases. A data set observed over a period of time is called a time series. A heteroscedastic time series is one where the conditional variability of an observation at the current time, given the past, depends on the past. Such data often arises in economics, finance, and physical sciences. In particular, an important example of long memory heteroscedastic time series is the volatility process in spot returns. It is also known that this volatility increases with bank interventions in currency markets. This intervention process is highly non-smooth time series since it is zero most of the times with certain bursts over some times. Part of the emphasis of the proposal is on developing optimal inferential procedures in a class of non-smooth non-linear heteroscedastic time series models. Another part emphasizes application of the results obtained to develop new tests of market efficiency and estimates of time dependent risk premium in financial economics and high frequency data mentioned in the proposal pertaining to German Mark and Swiss Frank vs. US Dollar exchange rates and commodity prices.