The main objectives of the project are to undertake additional extensions and refinements of the semi-nonparametric (SNP) approach to modeling multiple time series. The SNP approach is based on a Hermite series expansion of the conditional density of a strictly stationary multivariate process. The leading term is either a linear vector autoregressive model or an autoregressive conditional heteroskedastic model, with the choice depending upon the application. Higher order terms accommodate deviations from the leading term, including, for example, non-normalities or nonlinearities. The work is in two parts: a methodological section and an empirical section. The methodological work entails developing new ways to use the SNP approach for nonparametric structural estimation and to ascertain the dynamics embodied in an SNP estimate of the conditional density. The empirical work involves applications of SNP methods to issues in asset pricing and financial volatility. The main research tools for the empirical work are nonlinear maximum likelihood estimation and Monte Carlo simulation. The work will have an impact in several areas: documenting interesting regularities in financial time series data, forecasting turning points in economic data, and allowing estimation of what would previously be considered intractable models. Dissemination of the computer code developed by the project will be an important addition to the econometrics infrastructure.
