Frequency causality measures and Vector AutoRegressive (VAR) models: An improved subset selection method suited to parsimonious systems

Finding causal relationships in large dimensional systems is of key importance in a number of fields. Granger non-causality tests have become standard tools, but they only detect the direction of the causality, not its strength. To overcome this point, in the frequency domain, several measures have been introduced such as the Direct Transfer Function (DTF), the Partial Directed Coherence measure (PDC) or the Generalized Partial Directed Coherence measure (GPDC). Since these measures are based on a two-step estimation, consisting in i) estimating a Vector AutoRegressive (VAR) in the time domain and ii) using the VAR coefficients to compute measures in the frequency domain, they may suffer from cascading errors. Indeed, a flawed VAR estimation will translate into large biases in coherence measures. Our goal in this paper is twofold. First, using Monte Carlo simulations, we quantify these biases. We show that the two-step procedure results in highly inaccurate coherence measures, mostly due to the fact that non-significant coefficients are kept, especially in parsimonious systems. Based on this idea, we next propose a new methodology (mBTS-TD) based on VAR reduction procedures, combining the modified-Backward-in-Time selection method (mBTS) and the Top-Down strategy (TD). We show that our mBTS-TD method outperforms the classical two-step procedure. At last, we apply our new approach to recover the topology of a weighted financial network in order to identify through the local directed weighted clustering coefficient the most systemic assets and exclude them from the investment universe before allocating the portfolio to improve the return/risk ratio.