Dynamic update rule for the volatility spillover graph based on input realized volatility

Determine a principled procedure to update the volatility spillover graph (i.e., the adjacency matrix used to construct the magnetic Laplacian and perform the graph Fourier transform) as a function of the current input realized volatility windows in the GSPHAR framework, so that the graph reflects time-varying interconnections among stock market indices and can be integrated consistently into the forecasting pipeline.

Background

The GSPHAR framework incorporates the volatility spillover effect by constructing a directed volatility network via the Diebold–Yilmaz (DY) methodology and applying graph signal processing using the magnetic Laplacian. In the basic model, this adjacency matrix is precomputed from in-sample data and remains fixed during training.

Recognizing that volatility interconnections evolve over time, the authors introduce d-GSPHAR, which adjusts the DY-based adjacency matrix using absolute Pearson correlation matrices computed from mid-term and long-term input windows. While this offers a simple mechanism for adaptation, the authors explicitly note that the general problem of how to modify the volatility network in response to input realized volatility data remains unresolved.