PNAR (version 1.7)

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

Description

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

Usage

log_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.

Author

Mirko Armillotta, Michail Tsagris and Konstantinos Fokianos.

Details

This function computes initial values for the log-linear Poisson Network Autoregressive model of order \(p\) with \(q\) covariates (log-PNAR(\(p\))) with stationarity conditions. These initial values are simply the ordinary least squares estimators with a correction.

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

log_lin_estimnarpq

Examples

data(crime)
data(crime_W)
mod1 <- log_lin_narpq_init(crime, crime_W, p = 2)