Multivariate time series analysis considers more than one time series at the same time. It is a branch of multivariate statistical analysis, but deals specifically with dependent data. In general, it is much more complex than univariate time series analysis, especially when the number of series considered is large. In this book, we examine this more complex statistical analysis because in real life decisions often involve multiple interrelated factors or variables. Understanding the relationships between these factors and providing accurate estimates of these variables is valuable in decision making.
Multivariate linear regression models: statistical multi-factor models, transfer function models, multi-factor financial asset pricing models: Fama-French, Carhart etc.
Vector Autoregressive (VAR) and Vector Autoregressive Moving Average (VARMA) processes: basic assumptions and features, model selection criteria, estimation methods, estimation, VAR and VARMA models and structural analysis: Granger causality analysis, impulse response analysis, estimation error variance decomposition.
Cointegration processes, common stochastic trends, Vector Error Correction Models (VECM): cointegration tests (Johansen, Granger etc.), definition and model selection for VECM, estimation with VECM, structural analysis with VECM.
Multiple volatility and multivariate conditional variance (MGARCH) processes: MGARCH model types (CCC, DCC, BEKK), definitions and properties, estimation and estimation methods, volatility spillover effect.