Statistical analysis of financial econometric models

这项研究将检验各种金融计量经济学模型及其相关估计者的统计特性。具体地说，将研究两个主要领域：a)处理最优投资组合配置的模型。这里的目的是研究最优投资组合权重的分布或这些权重的某个标量函数。由于权重是参数二次规划问题的结果，因此通常通过蒙特卡罗模拟来检验它们的性质。过去的模拟研究表明，权重通常是严重偏向的。为了确定偏差的来源，从而找到减少偏差的方法，需要考虑准确的矩和权重的准确分布。研究将考虑关于资产收益向量的各种多变量分布假设，以及对权重的现实和实际相关的约束。虽然在多元正态分布的简单情形下已经取得了一些进展，但是其他的分布假设和非负约束没有被考虑；这些将是本研究的主题。b)涉及随机波动率的模型。多年来，这些模型一直对计量经济学家构成重大挑战，因为它们的公式涉及一个未观察到的(潜在)变量--波动率。从实践的角度来看，已经有许多可供选择的规范，每个规范都声称能够更好地捕捉数据的各种风格化事实。对这些模型中的许多还没有进行详细的分析统计分析。因此，拟议研究的这一部分将旨在系统地检查这些模型，得出准确的统计特性，如矩和特征函数。这些结果将使人们更清楚地了解这些模型的动态，并改进估计。

This research will examine the statistical properties of various financial econometric models along with their associated estimators. In particular there will be two broad areas examined:a)models dealing with optimal portfolio allocation.Here the aim is to examine the distribution of the optimal portfolio weights or some scalar function of these weights. Since the weights are the result of a parametric quadratic programming problem, their properties are usually examined via Monte Carlo simulation. Past simulation studies have shown that the weights are usually severly biased. In order to ascertain the source of the bias and hence ways to reduce it one needs to consider the exact moments and the exact distribution of the weights.The research will consider various multivariate distributional assumptions on the vector of asset returns along with realistic and practically relevant constraints on the weights. While some progress has been made in simple cases under multivariate normality other distributional assumptions and non-negativity constraints have not been considered; these will be the subject of this research.b)models involving stochastic volatility.The research here will examine stochastic volatility (SV) models formulated in both discrete and continuous time. These models have, for many years, posed a major challenge to econometricians since their formulation involves an unobserved (latent) variable, the volatility. From a practical point there have been many alternative specifications each claiming to better capture various stylized facts of the data. Detailed analytical statistical analysis of many of these models has not been undertaken. Consequently, this section of the proposed research will aim to systematically examine these models, deriving exact statistical properties such as moments and characteristic functions. The results will enable a clearer understanding of the dynamics of these models and lead to improved estimation.