PNAR (version 1.7)

lin_ic_plot: Scatter plot of information criteria versus the number of lags in the linear Poisson NAR(p) model model with p lags and q covariates (PNAR(p))

Description

Scatter plot of information criteria versus the number of lags in the linear Poisson Network Autoregressive model of order \(p\) with \(q\) covariates (PNAR(\(p\))).

Usage

lin_ic_plot(y, W, p = 1:10, Z = NULL, uncons = FALSE, ic = "QIC")

Value

A scatter plot with the lag order versus either QIC (default), AIC or BIC, and a vector with their values, for each lag order.

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

A vector with integer numbers, the range of lags in the model, for which the AIC, BIC and QIC will be computed.

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.

uncons

Logical, if TRUE an unconstrained optimization without stationarity constraints is performed (default is FALSE).

ic

The information criterion you want to plot, "QIC" (default value), "AIC" or "BIC".

Author

Mirko Armillotta, Michail Tsagris and Konstantinos Fokianos.

Details

The function computes the AIC, BIC or QIC for a range of lag orders of the linear Poisson Network Autoregressive model of order \(p\) with \(q\) covariates (PNAR(\(p\))).

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, log_lin_ic_plot

Examples

data(crime)
data(crime_W)
lin_ic_plot(crime, crime_W, p = 1:3)