Gaussian and Student-t Copula Models for Count Time Series

Provides likelihood-based inference for Gaussian and Student-t copula models for univariate count time series. Supports Poisson, negative binomial, binomial, beta-binomial, and zero-inflated marginals with ARMA dependence structures. Includes simulation, maximum-likelihood estimation, residual diagnostics, and predictive inference. Implements Time Series Minimax Exponential Tilting (TMET) , an adaptation of minimax exponential tilting of Botev (2017) . Also provides a linear-cost implementation of the Geweke–Hajivassiliou–Keane (GHK) simulator following Masarotto and Varin (2012) , and the Continuous Extension (CE) approximation of Nguyen and De Oliveira (2025) . The package follows the S3 design philosophy of 'gcmr' but is developed independently.

output: github_document

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, including:

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 through ARMA(p, q) processes.

Likelihood evaluation is available through 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:

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(link = "log"),
  cormat = arma.cormat(p = 1, q = 0),
  method = "TMET",
  family = "gaussian",
  options = gctsc.opts(seed =1, M = c(100,1000))
)

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. and De Oliveira, V. (2026). Approximating Gaussian Copula Models for Count Time Series: Connecting the Distributional Transform and a Continuous Extension. Journal of Applied Statistics, 53, 1--22.

Nguyen, Q. N. and De Oliveira, V. (2026). Likelihood Inference in Gaussian Copula Models for Count Time Series via Minimax Exponential Tilting. Computational Statistics and Data Analysis, 218, 108344.

Nguyen, Q. N. and De Oliveira, V. (2026). Scalable Likelihood Inference for Student--t Copula Count Time Series. Stats, 9, 1--49.