local_relevance_plot function

Produces a local neighbourhood relevance plot based on the distances in the underlying network.

Produces a local neighbourhood relevance plot based on the distances in the underlying network. The heat-map matrix should reflect clusters if a GNAR model is valid. The size of the clusters depends on the maximum r-stage depth for neighbourhood regression, as $r^*$ gets larger, the clusters grow or intersect and cover more nodes. The relative strength of conditionally correlated nodes is $\mathrm{rscc} (i, j) := \{ d(i,j) \}^{-1} \mathbb{I} \{ d(i, j) \leq r^* \} + \{2 d(i,j) \}^{-1} \mathbb{I} \{ r^* < d(i, j) \leq 2 r^* \}$.

local_relevance_plot(network, r_star)
  cross_correlation_plot(h, vts)

Arguments

• network: GNAR network object, which is the underlying network for the time series under study.
• r_star: Maximum active r-stage depth for neighbourhood regression.
• h: The lag in the cross correlation plot.
• vts: The vector time series to compute the cross correlation plot on.

Returns

Produces the local relevance plot. 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 a local relevance plot, which is a heat-map matrix from a stationary 
# GNAR(1, [1]) simulation.
#
gnar_simulation <- GNARsim(n = 100, net=fiveNet, alphaParams = list(rep(0.35, 5)), 
        betaParams = list(c(0.25)), sigma=1)
# Active node plot
local_relevance_plot(fiveNet, 1)
# Compare to the cross-correlation plot at one-lag
cross_correlation_plot(1, gnar_simulation)