Graphical Models for the Identification of Causal Structures in Multivariate Time Series Models

In this paper we present a semi-automated search procedure to deal with the problem of the identification of the contemporaneous causal structure connected to a large class of multivariate time series models. We refer in particular to multivariate models, such as vector autoregressive (VAR) and dynamic factor (DF) model, in which the background or theoretical knowledge is not sufficient or enough reliable to build a structural equations model. VAR models deal with a small number of time series models (the maximum number is typically between 6 and 8), while DF models deal with a large number of time series, possibly larger than the number of observation (T ) over time. Both VAR and DF models have proven to be very efficient in the macroeconomic and financial literature to address different empirical issues, such as forecasting, summarizing the statistical properties of the data, and building economics indicators (of business cycles, for instance). Moreover, DF models can be used in the financial literature to estimate insurable risk and in the macroeconomic literature to learn about aggregate behavior on the basis of microeconomic data (sectors, regions). (Forni and Lippi (1997), Forni et al. (2000), and Stock and Watson (2001) are useful references).