In this chapter, we review nonlinear models for vector time series data and develop new nonparametric estimation and inference for them. Vector time series data exist widely in practice. In financial markets, multiple time series are usually correlated. When analyzing several interdependent time series, in general one should consider them as a single vector time series fitted by multivariate models, which provides a useful tool for modeling interdependencies among multiple time series and for simultaneously analyzing feedback and Granger causality effects. Since nonlinear features are widely observed in time series, we consider nonlinear methodology for modeling nonlinear vector time series data, which allows flexibility in the model structure and avoids the curse of dimensionality.
Part of the book: Time Series Analysis and Applications