gctsc

gctsc provides fast and scalable likelihood inference for Gaussian and Student–t copula models for count time series.

The package supports a wide range of discrete marginals:

• Poisson
  
• Negative Binomial
  
• Binomial
  
• Beta Binomial
  
• Zero-Inflated Poisson (ZIP)
  
• Zero-Inflated Binomial (ZIB)
  
• Zero-Inflated Beta-Binomial (ZIBB)

The latent dependence structure is modeled via ARMA(p, q) processes.

Likelihood evaluation is performed using one of the following approximation methods:

• TMET — Time Series Minimax Exponential Tilting
  
• GHK — Geweke–Hajivassiliou–Keane simulator
  
• CE — Continuous Extension

The implementation exploits ARMA structure for efficient high-dimensional computation.

Additional features include:

• Simulation utilities
  
• Randomized quantile residual diagnostics
  
• Predictive distributions and scoring rules (CRPS, LOGS)

Installation

From CRAN (after release):

install.packages("gctsc"

From Github: remotes::install_github(“QNNHU/gctsc”)

Quick Example:

library(gctsc)

# Simulate Poisson AR(1) data under a Gaussian copula
set.seed(1)
y <- sim_poisson(
  mu = 5,
  tau = 0.5,
  arma_order = c(1, 0),
  nsim = 300,
  family = "gaussian"
)$y

# Fit model
fit <- gctsc(
  y ~ 1,
  data = data.frame(y = y),
  marginal = poisson.marg(),
  cormat = arma.cormat(p = 1, q = 0),
  method = "TMET",
  family = "gaussian",
  options = gctsc.opts(M = 1000)
)

summary(fit)

# Diagnostic plots
plot(fit)

# One-step prediction
predict(fit)

What Makes gctsc Different?

Compared to existing implementations, gctsc added:

• Exploits ARMA structure for scalable likelihood evaluation in time series settings

• Supports zero-inflated marginals with flexible covariate specification, including seasonal components

• Implements scalable minimax exponential tilting (TMET) for efficient likelihood approximation

• Provides a linear-cost GHK importance sampling implementation

• Implements fast continuous extension method

• Supports Student–t copulas for modeling heavy-tailed dependence

• Computes full predictive distributions for discrete time series

References

If you use this package in published work, please cite:

Nguyen, Q. N., & De Oliveira, V. (2026). Approximating Gaussian copula models for count time series: Connecting the distributional transform and a continuous extension. Journal of Applied Statistics.

Nguyen, Q. N., & De Oliveira, V. (2026). Likelihood Inference in Gaussian Copula Models for Count Time Series via Minimax Exponential Tilting. Computational Statistics & Data Analysis.

Nguyen, Q. N., & De Oliveira, V. (2026). Scalable Likelihood Inference for Student–t Copula Count Time Series. Manuscript in preparation.