Statistical analysis of financial econometric models

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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.