Statistical analysis of financial econometric models

本研究将检验各种金融计量经济模型及其相关估计器的统计特性。特别地，将有两个广泛的领域进行研究：a)处理最佳投资组合分配的模型。这里的目的是检验最优投资组合权重的分布或这些权重的标量函数。由于权重是参数二次规划问题的结果，因此它们的性质通常通过蒙特卡罗模拟来检验。过去的仿真研究表明，权重通常存在严重偏差。为了确定偏差的来源和减少偏差的方法，需要考虑准确的力矩和权重的准确分布。本研究将考虑资产收益向量的各种多元分布假设以及对权重的现实和实际相关约束。虽然在多元正态性的简单情况下取得了一些进展，但没有考虑其他分布假设和非负性约束；这些将是本研究的主题。B)涉及随机波动的模型。这里的研究将检验在离散和连续时间下制定的随机波动（SV）模型。多年来，这些模型对计量经济学家构成了重大挑战，因为它们的公式涉及一个未观察到的（潜在的）变量，即波动性。从实用的角度来看，有许多可选的规范，每个规范都声称可以更好地捕获数据的各种程式化事实。尚未对其中许多模型进行详细的分析统计分析。因此，本节提出的研究将旨在系统地检查这些模型，得出精确的统计特性，如矩和特征函数。结果将使对这些模型的动力学有更清晰的理解，并导致改进的估计。

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.