A note on normalization schemes: the case of generalized forecast error variance decomposition

The aim of this paper is to propose new normalization schemes for the values obtained from the generalized forecast error variance decomposition, in order to obtain more reliable net spillover measures. We provide a review of various matrix normalization schemes used in different application domains. The intention is to contribute to the financial econometrics literature aimed at building a bridge between different approaches able to detect spillover effects, such as spatial regressions and network analyses. Considering DGPs characterized by different degrees of correlation and persistence, we show that the popular row normalization scheme proposed by Diebold and Yilmaz (2012), as well as the alternative column normalization scheme, may lead to inaccurate measures of net contributions (NET spillovers) in terms of risk transmission. Results are based on simulations and show that the number of errors increases as the correlation between the variable increases. The normalization schemes we suggest overcome these limits.