Time series released by statistical offices do not obviously have the same publication frequency. Most national account data (consumption, investment, etc) are available quarterly while business cycle indicators such as the industrial production index, the unemployment rate or the price level are available monthly. Some series are produced weekly (money stock) and many financial variables are usually daily, or even intra daily. A common practice when building a multivariate model using series with different frequencies (e.g., in a VAR) is to aggregate every variable at the low frequency level, hence potentially deleting some important high frequency information. In order keep those data, Ghysels (2012) has introduced an observable mixed frequency VAR framework. This new modelling consists in stacking the low frequency variable with the high frequency series that correspond to that low frequency variable and to estimate a (mixed frequency) VAR. As an example, in Hecq, Goetz and Urbain (2013) we set up a VAR with the quarterly GDP and 3 monthly industrial production variables in a four dimensional VAR system. This new framework can be quite interesting to test for causality between low and high frequency variables as well as for forecasting. However, the issue becomes much more cumbersome when we consider for instance the quarterly GDP and 60 daily interest rates. To this end we propose in this paper to investigate several reduction techniques for this particular big dimensional system. We compare the forecasting performances as well as the results for Granger causality tests of the (i) unrestricted VAR, (ii) the restricted VARX(1) recently proposed by Ghysels, (iii) a system of MIDAS equations and (iv) a reduced rank approach consisting in determining and imposing a few common dynamics generating the system (common cycles). We compare the different approaches both using Monte Carlo simulations and on empirical analyses for the link between business cycle fluctuations and financial market volatilities.

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