Chapter 16. Copula Methods for Forecasting Multivariate Time Series Copula based models provide a great deal of flexibility in modeling multivariate distributions allowing the researcher to specify the models for the marginal distributions separately from the dependence structure (copula) that links them to form a joint distribution. In addition to flexibility this often also facilitates estimation of the model in stages reducing the computational burden. This chapter reviews the growing literature on copula based models for economic and financial time series data and discusses in detail methods for estimation inference goodness of fit testing and model selection that are useful when working with these models. A representative data set of two daily equity index returns is used to illustrate all of the main results.