Statistical Inference on Multivariate Nonlinear Time Series Models : Simulation Based Approach

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Combined forecasts from a linear and a nonlinear model are investigated for time series with possibly nonlinear characteristics. The forecasts are combined by a constant coefficient regression method as well as a time varying method. The time varying method allows for a locally (non)linear model. The methods are applied to data from two kinds of disciplines : the Canadian lynx and sunspot series from the natural sciences, and Nelson-Plosser's U.S. series from economics. It is shown that the combined forecasts perform well, especially with time varying coefficients. This result holds for out of sample performance for the sunspot and Canadian lynx number series, but it does not uniformly hold for economic time series.Further this project considered a framework of testing continuous time nonlinear business cycle models by using discrete observations through time discretization in terms of "Local Linearization(L.L.)" method. We employ a Bayesian inference on the conditions for the models to be valid as business cycle models, which are represented in the form of inequality of some function of parameters. A computationally efficient algorithm of Monte Carlo integration for that problem is proposed and applied to data of the U.S. and Japan.Finally, for analyzing multivariate market share time series, I proposed a dynamic market share model with "logical consistency" by using Bayesian VAR model. The proposed method makes it possible to forecast not only the values of market share by themselves, but also various dynamic market share relations across different brands or companies.