Causal Dynamic Complex Networks

The Granger-Causal Dynamic Complex Networks model (GCDCN 1.0) provides an easy way to analyse the dynamic causal co-movements of a system of time series variables.

In energy economics, this model is currently used to investigate the effectiveness of transmission networks in delivering energy price synchronisation.

This model extends the principle of Granger-causality to cover a whole system of variables rather than simply studying their bivariate causal interface. The software analyses how a system of variables evolves over time by uncovering the system-wide synchronicity of the group of time series variables involved, as well as allowing the user to discover the incoming and outgoing causal interface of one variable or a group of variables in a network.

The model is based on the well-known economic principle of bivariate Granger causality (Granger, 1969), which was firstly implemented by Barnett and Seth (2014) for application to neurological data.

Castagneto-Gissey et al. (2014) first developed this method for use in a dynamic networks context and applied it to energy and economics to understand whether the commissioning of novel interconnection infrastructure was reflected throughout an improved degree of synchronisation of electricity spot prices between European Union markets. This study showed that not only did causal patterns among EU electricity prices considerably increase after market widening but also that dynamic networks are an efficient tool for modelling electricity market integration.

The model creates the network and analyses it, providing a variety of network indices, including:

  • In-degrees, or in-strengths, for each variable considered (i.e. the incoming causal interface to a given variable, showing which other variables in the network Granger-cause the given variable) and for each specified time window.
  • Out-degrees, or out-strengths, for each variable considered (i.e. the outgoing causal interface to a given variable, showing which other variables are Granger-caused by that variable) and for each specified time window.
  • Global connection density (i.e. the whole system's Granger-causal interface. For example, in a network of EU electricity spot prices, this measure informs about the time-varying integration of the EU electricity spot market).

The model may be used with deterministic and stochastic variable types. It is user-friendly and very flexible with regards to the input of a variety of model parameters, and shall be used on MATLAB 2009 and newer versions of the software. Our package includes a step-by-step instructions manual to facilitate your use of the model source code. The manual is available, at present, in three languages: English, Spanish and Italian.

Importantly, this model may not only be used to study energy variables, but also more generally economic variables. The model can also be applied to study neuroscientific, clinical, social and engineering variables, in addition to internet-related and social networks, including a variety of other systems.

Please contact us if you have any questions about the GCDCN package or model.

Model summary

Type: A multivariate dynamic complex network model extending pairwise Granger-causality to cover an entire, evolving system of variables.

(i) Unveiling the time-varying synchronicity of a group of similar variables.

(ii) Understanding how a group of variables in a network causally interact over time.

(iii) Exploring the incoming and outgoing causal interface of one variable or a group of variables in a network.

Policy impact A policy decision support tool, enabling DNOs and TNOs, among other market agents, to monitor energy flows, observe the synchronisation of prices and detect market integration in a given network.
Spatial scale: Regional, national, continental or any interconnected spatial scale where all variables refer to a single market (e.g., all national electricity markets in the European Union, or all regional markets for a given commodity in the UK)
Temporal scale: Any temporal scale (half-hourly, hourly, daily, weekly, monthly, annual).
Main contacts: Dr Giorgio Castagneto-Gissey (UCL), Dr Elena Previti (KCL)


The GCDCN source code and manual are available for academic, personal and other non-commercial use.


Academic Papers

Castagneto-Gissey, G., Chavez, M., & Fallani, F. D. V. (2014). Dynamic Granger-causal networks of electricity spot prices: A novel approach to market integration. Energy Economics, 44, 422-432.

Conference Papers

Castagneto-Gissey, G., De Vico Fallani, F. & Chavez, M. (2013). Causal Connectivity in European electricity spot price dynamics: A network theoretical approach, 13th European Conference of the International Association for Energy Economics (Dusseldorf, Germany).