active_node_plot function

Produces an active node matrix heat-map.

Produces an active node matrix heat-map, which compares the local impact each node has on all the other ones (i.e., regressing $j$ on $i$) once a model order has been chosen. The local relevance indes is $\mathrm{local} (i, j) := \bigg ( w_{ij} \sum_{k = 1}^{p} |\hat{\beta}_{kr}| \bigg ) \bigg \{ \sum_{l \in \mathcal{N} (i)} \sum_{r = 1}^{r^*} \sum_{k = 1}^{p} w_{il} |\hat{\beta}_{kr}| \bigg) \bigg \}^{-1},$

which is closer to one the more relevant $j$ is when forecasting $i$.

active_node_plot(vts, network, max_lag, r_stages)

Arguments

• vts: Vector time series under study.
• network: GNAR network object, which is the underlying network for the time series under study.
• max_lag: Maximum lag of the fitted GNAR model - i.e., $\mathrm{GNAR}(p, [s_1, \dots, s_p]).$
• r_stages: Neighbourhood regression oreder of the fitted GNAR model - i.e., $(s_1, \dots, s_p)$.

Returns

Produces the local influence matrix heat-map for a specific model order. Does not return any values.

Author(s)

Daniel Salnikov and Guy Nason

References

Nason, G.P., Salnikov, D. and Cortina-Borja, M. (2023) New tools for network time series with an application to COVID-19 hospitalisations. https://arxiv.org/abs/2312.00530

Examples

#
# Produces an active node heat-map matrix from a stationary GNAR(2, [2, 1]) simulation.
#
gnar_simulation <- GNARsim(n = 100, net=fiveNet,
        alphaParams = list(rep(0.25, 5), rep(0.12, 5)), 
        betaParams = list(c(0.25, 0.13), c(0.20)), sigma=1)
#
# Active node plot
#
active_node_plot(gnar_simulation, fiveNet, 2, c(2, 1))