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都表现出长期记忆，即它们作为滞后的函数的自协方差随着滞后接近无穷大而以双曲线速度减小到零。这样的过程在原点具有无限的光谱密度。这一建议的一部分涉及在半参数设置下，在存在可能具有长记忆性的回归或解释协变量的情况下，为异方差、非光滑、非线性时间序列模型开发渐近最优和稳健估计。特别是，当非光滑自回归模型中存在长记忆解释变量且误差分布未知时，计划获得这些模型所产生的实验的极限。在第二部分中，PI/Co-PI提出了对异方差平稳遍历时间序列拟合参数自回归均值和/或分位数函数的渐近分布自由检验。这些检验预期是不涉及非参数曲线估计的部分和过程的某些鞅变换的函数。PI/Co-PI还计划与现有的一些测试进行比较研究。获得的结果将被用于估计感兴趣的参数和测试与金融经济学问题相关的理论。如果远距离观测之间的关联随着观测之间的距离增加而缓慢衰减但持续存在，则数据集被称为具有长期记忆力。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，观测值在当前时间的条件变异性取决于过去。这样的数据通常出现在经济学、金融学和自然科学中。特别是，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。人们还知道，随着银行干预外汇市场，这种波动性会增加。这种干预过程是高度非平稳的时间序列，因为它在大多数时间是零的，在某些时间具有一定的突发性。该建议的部分重点是在一类非光滑、非线性、异方差的时间序列模型中开发最优推理过程。另一部分侧重于应用所获得的结果来开发金融经济学中关于德国马克和瑞士马克对美元汇率和商品价格的提案中提到的具有时间依赖性的风险溢价和高频数据的新的测试和估计。

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.