GNARXsim {GNAR}

Simulates a GNARX process

Description

Simulates a GNAR process with Normally distributed innovations.

Usage

GNARXsim(n=200, net=GNAR::fiveNet, alphaParams=list(c(rep(0.2,5))),
	betaParams=list(c(0.5)), sigma=1, tvnets=NULL, netsstart=NULL, xvts=NULL, 
	lambdaParams=NULL)

Arguments

n

time length of simulation.

net

network used for the GNAR simulation.

alphaParams

a list containing vectors of auto-regression parameters for each time-lag.

betaParams

a list of equal length as alphaParams containing the network-regression parameters for each time-lag.

sigma

the standard deviation for the innovations.

tvnets

a list of additional networks. Currently only NULL (the static network case) is supported.

netsstart

a vector of times corresponding to the first time points for each network of tvnets. Currently only NULL (the static network case) is supported.

xvts

a list of matrices containing values of the exogenous regressors for each vertex/node. The i,j entry of the hth element of the list refers to the value of the hth exogenous regressor for time i and vertex/node j.

lambdaParams

a list containing vectors of parameters associated to effect of the exogenous regressor variables for each time-lag.

Details

Parameter lists should not be NULL, set unused parameters to be zero. See GNARXfit for model description.

Value

GNARXsim returns the multivariate time series as a ts object, with n rows and a column for each of the nodes in the network.

References

Knight, M.I., Nunes, M.A. and Nason, G.P. Modelling, detrending and decorrelation of network time series. arXiv preprint.

Knight, M.I., Leeming, K., Nason, G.P. and Nunes, M. A. (2020) Generalised Network Autoregressive Processes and the GNAR package. Journal of Statistical Software, 96 (5), 1–36.

Nason G.P. and Wei J. (2022) Quantifying the economic response to COVID-19 mitigations and death rates via forecasting Purchasing Managers’ Indices using Generalised Network Autoregressive models with exogenous variables. Journal of the Royal Statistical Society Series A, 185, 1778–1792.

Examples

#Simulate a GNARX process with the fiveNet network

set.seed(1)
n = 1000
xvts=list()
xvts[[1]] = matrix(rnorm(5*n, mean=0, sd=2), nrow=n, ncol=5)
xvts[[2]] = matrix(rnorm(5*n, mean=0, sd=2), nrow=n, ncol=5)
lambdaParams=list()
lambdaParams[[1]] = c(0.5, -0.5)
lambdaParams[[2]] = c(0.3, 0.1)

# Simulate the GNARX using the exogenous variables xvts with associated parameters lambdaParams
 
Y_data <- GNARXsim(n=n, net=GNAR::fiveNet, alphaParams=list(c(rep(0.2,5))), betaParams=list(c(0.5)),
                      sigma=1, xvts=xvts, lambdaParams=lambdaParams)

# now try to refit the model
 
model <- GNARXfit(vts = Y_data, net = GNAR::fiveNet,globalalpha = TRUE, alphaOrder = 1, 
		betaOrder = 1, xvts = xvts, lambdaOrder = c(1,1))

model