lin_narpq_init {PNAR}

Starting values for the linear Poisson NAR(p) model model with p lags and q covariates (PNAR(p))

Description

Starting values for the linear Poisson Network Autoregressive model of order p with q covariates (PNAR(p)).

Usage

lin_narpq_init(y, W, p, Z = NULL)

Arguments

y

A TT x N time series object or a TT x N numerical matrix with the N multivariate count time series over TT time periods.

W

The N x N row-normalized non-negative adjacency matrix describing the network. The main diagonal entries of the matrix should be zeros, all the other entries should be non-negative and the maximum sum of elements over the rows should equal one. The function row-normalizes the matrix if a non-normalized adjacency matrix is provided.

p

The number of lags in the model.

Z

An N x q matrix of covariates (one for each column), where q is the number of covariates in the model. Note that they must be non-negative.

Details

The function computes starting values to be used in the function lin_estimnarpq. These are simply the ordinary least squares estimators with a correction. If any of the the resulting coefficients is negative they become equal to 0.001

Value

A vector with the initial values.

Author(s)

Mirko Armillotta, Michail Tsagris and Konstantinos Fokianos.

References

Armillotta, M. and K. Fokianos (2022). Poisson network autoregression. https://arxiv.org/abs/2104.06296

See Also

lin_estimnarpq

Examples

data(crime)
data(crime_W)
x0 <- lin_narpq_init(crime, crime_W, p = 2)