Mixture models for financial assets

Abstract

This dissertation is primarily concerned with mixture models for high-dimensional financial data. New flexible mixture models are introduced and implemented with fast and effective optimization routines. The stochastic gradient approach uses random gradients to update the parameters of the mixture model improving the chance of the iterates converging to a higher mode. Chapter 2 provides the details of the stochastic gradient optimization routines used. Chapter 3 suggests two new multivariate density estimators, namely the marginal adaptation mixture of normals and the mixture of normals copula. Their performances are compared with a few recent popular models such as the skewed-t model. Chapter 4 discusses covariance estimation for high dimensional data. The aim of the chapter is to improve the estimation of covariance matrices by using mixture shrinkage priors. This chapter also shows how to apply the priors to the simultaneous estimation of several covariance matrices such as in the case of mixture of normals models. Chapters 5 and 6 consider the estimation or fitting of models to time series data, when the models may experience a small number of structural breaks. Chapter 5 looks at univariate data and Chapter 6 considers multivariate data. In particular, Chapter 6 shows how to estimate a Gaussian vector autoregressive model subject to occasional structural breaks using a mixture of experts framework.