PNAR (version 1.7)

lin_narpq_init: 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)

Value

A vector with the initial values.

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.

Author

Mirko Armillotta, Michail Tsagris and Konstantinos Fokianos.

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.

References

Armillotta, M. and K. Fokianos (2023). Nonlinear network autoregression. Annals of Statistics, 51(6): 2526--2552.

Armillotta, M. and K. Fokianos (2024). Count network autoregression. Journal of Time Series Analysis, 45(4): 584--612.

Armillotta, M., Tsagris, M. and Fokianos, K. (2024). Inference for Network Count Time Series with the R Package PNAR. The R Journal, 15/4: 255--269.

See Also

lin_estimnarpq

Examples

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