Daily aggregated weather measurements for KCWC station

Description

Daily aggregated weather measurements for KCWC station

Usage

data("KCWC")

Format

A data frame with 2665 rows and 4 variables.

ARMA Correlation Structure for Copula Count Time Series Models

Description

Constructs an ARMA(p,q) correlation structure for use in Gaussian and Student–t copula count time series models.

Usage

arma.cormat(p = 0, q = 0, tau.lower = NULL, tau.upper = NULL)

Arguments

Details

The ARMA model specifies the dependence structure of the latent copula process.

The ARMA parameters must define a stationary and invertible process. These conditions are enforced during model fitting.

Value

An object of class "arma.gctsc" and "cormat.gctsc" containing:

• npar: Number of ARMA parameters (p + q).

• od: Integer vector c(p, q).

• start: Function to compute starting values from data, typically using arima.

• lower, upper: Parameter bounds.

See Also

gctsc, poisson.marg, predict.gctsc

Weekly Campylobacter case counts across Germany

Description

Weekly Campylobacter case counts across Germany

Usage

data("campyl")

Format

A data frame with 1248 rows and 413 variables.

Extract Coefficients from a gctsc Model

Description

Returns the estimated coefficients from a fitted gctsc model object.

Usage

## S3 method for class 'gctsc'
coef(object, ...)

Arguments

Value

A named numeric vector of model coefficients.

Fit a Copula-Based Count Time Series Model

Description

Fits a Gaussian or Student–t copula model to univariate count time series with discrete marginals (Poisson, negative binomial, binomial/beta–binomial, and zero–inflated variants) and latent dependence specified via ARMA correlation structures.

Usage

gctsc(
  formula = NULL,
  data,
  marginal,
  cormat,
  method = c("TMET", "GHK", "CE"),
  c = 0.5,
  QMC = TRUE,
  pm = 30,
  start = NULL,
  family = c("t", "gaussian"),
  df = 10,
  options = gctsc.opts()
)

Arguments

Details

The high-dimensional rectangle probability defining the copula likelihood is approximated using one of:

• TMET (Time Series Minimax Exponential Tilting),

• GHK (Geweke–Hajivassiliou–Keane simulation), or

• CE (Continuous Extension).

The interface mirrors glm(). Zero–inflated marginals accept a named list of formulas, e.g., list(mu = y ~ x, pi0 = ~ z). Non–zero–inflated marginals accept a single formula or list(mu = ...).

Formulas. For zero–inflated marginals, if neither mu nor pi0 is supplied, both default to intercept–only models (mu ~ 1, pi0 ~ 1). If mu is supplied but pi0 is missing, pi0 ~ 1 is used.

Dependence. The ARMA parameters are encoded in cormat. Models must satisfy stationarity and invertibility conditions. ARMA(0,0) is not supported.

Method-specific notes. CE ignores QMC and options$M. GHK and TMET require options$M to be a positive integer. TMET additionally uses pm when q > 0.

Value

An object of class "gctsc" containing, among others:

• coef: parameter estimates,

• maximum: approximate log–likelihood at the optimum,

• se: standard errors when available,

• terms, model, call: model metadata.

References

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

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

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.

See Also

arma.cormat, poisson.marg, zib.marg, zibb.marg, gctsc.opts

Examples

## Example 1: Gaussian copula, Poisson marginal, AR(1)
set.seed(42)
n <- 500
sim_dat <- sim_poisson(mu = 10, tau = 0.3, arma_order = c(1, 0),
                       nsim = n, family = "gaussian")

dat <- data.frame(y = sim_dat$y)

fit_gauss <- gctsc(
  y ~ 1,
  data = dat,
  marginal = poisson.marg(lambda.lower = 0),
  cormat = arma.cormat(p = 1, q = 0), family = "gaussian",
  method = "CE",
  options = gctsc.opts(M = 1000, seed = 42)
)
summary(fit_gauss)

## Example 2: Student--t copula
sim_dat_t <- sim_poisson(mu = 10, tau = 0.3, arma_order = c(1, 0),
                         nsim = 500, family = "t", df = 10)

dat_t <- data.frame(y = sim_dat_t$y)

fit_t <- gctsc(
  y ~ 1,
  data = dat_t,
  marginal = poisson.marg(lambda.lower = 0),
  cormat = arma.cormat(p = 1, q = 0), family ="t",
  df= 10, method = "CE",
  options = gctsc.opts(M = 1000, seed = 42)
)
summary(fit_t)

Set Options for Gaussian and Student t Copula Time Series Model

Description

Creates a control list for simulation and likelihood approximation in the Gaussian ad Student t copula model, including the random seed and Monte Carlo settings.

Usage

gctsc.opts(seed = NULL, M = 1000, ...)

Arguments

Value

A list with components:

Marginal Models for Copula Time Series

Description

The following marginal models are currently available:

poisson.marg(link = "log")

Poisson distribution.

negbin.marg(link = "log")

Negative binomial distribution.

binom.marg(link = "logit", size)

Binomial distribution with fixed number of trials.

bbinom.marg(link = "logit", size)

Beta-binomial with overdispersion.

zip.marg(link = "log")

Zero-inflated Poisson model.

zib.marg(link = "logit", size)

Zero-inflated binomial.

zibb.marg(link = "logit", size)

Zero-inflated beta-binomial with separate covariates for zero inflation.

Usage

poisson.marg(link = "identity", lambda.lower = NULL, lambda.upper = NULL)

binom.marg(link = "logit", size = NULL, lambda.lower = NULL, lambda.upper = NULL)

zib.marg(link = "logit", size = NULL, lambda.lower = NULL, lambda.upper = NULL)

negbin.marg(link = "identity", lambda.lower = NULL, lambda.upper = NULL)

zip.marg(link = "identity", lambda.lower = NULL, lambda.upper = NULL)

bbinom.marg(link = "logit", size, lambda.lower = NULL, lambda.upper = NULL)

zibb.marg(link = "logit", size,  lambda.lower = NULL, lambda.upper = NULL)

Arguments

Details

These functions define the marginal distributions used in copula-based count time series models.

Each marginal constructor returns an object of class "marginal.gctsc" which defines:

• start: a function to compute starting values.

• npar: number of parameters.

• bounds: truncation bounds on the latent Gaussian.

These marginals are designed to work with gctsc() and its related methods.

Value

A list of class "marginal.gctsc" representing the marginal model.

References

Cribari-Neto, F. and Zeileis, A. (2010). Beta regression in R. Journal of Statistical Software, 34(2): 1–24.

Ferrari, S.L.P. and Cribari-Neto, F. (2004). Beta regression for modeling rates and proportions. Journal of Applied Statistics, 31(7): 799–815.

Masarotto, G. and Varin, C. (2012). Gaussian copula marginal regression. Electronic Journal of Statistics, 6: 1517–1549.

See Also

gctsc, predict.gctsc, arma.cormat

Examples

poisson.marg(link = "identity")
zibb.marg(link = "logit", size = 24)

Diagnostic Plots for Fitted Copula Count Time Series Models

Description

Produces diagnostic plots for a fitted Gaussian or Student–t copula count time series model of class "gctsc".

The diagnostics are based on randomized quantile residuals and probability integral transform (PIT) values.

Usage

## S3 method for class 'gctsc'
plot(
  x,
  caption = rep("", 5),
  main = rep("", 5),
  level = 0.95,
  col.lines = "gray",
  ...
)

Arguments

Details

The following diagnostic plots are produced:

1. Time series of randomized quantile residuals.

2. Q–Q plot against the reference distribution.

3. Histogram of PIT values.

4. Autocorrelation function (ACF) of residuals.

5. Partial autocorrelation function (PACF) of residuals.

For Gaussian copulas, residuals are compared against the standard normal distribution. For Student–t copulas, residuals are compared against a Student–t distribution with degrees of freedom obtained from fitted model.

Value

Invisibly returns NULL.

This function is called for its side effects and returns invisible().

See Also

residuals.gctsc

residuals.gctsc for computing the residuals used in the plots.

Examples

# Simulate data from a Poisson AR(1) model
set.seed(123)
n <- 2000
mu <- 5
phi <- 0.5
arma_order <- c(1, 0)
y <- sim_poisson(mu = mu, tau = phi, arma_order = arma_order, nsim = n)$y

# Fit the model using the CE method
fit <- gctsc(y~1,
  marginal = poisson.marg(link = "identity", lambda.lower = 0),
  cormat = arma.cormat(p = 1, q = 0), family ="gaussian",
  method = "CE",
  options = gctsc.opts(seed = 1, M = 1000),
  c = 0.5
)

# Produce diagnostic plots
par(mfrow = c(2, 3), ask = FALSE)
plot(fit)

Approximate Log-Likelihood via Continuous Extension (CE)

Description

Computes the approximate log-likelihood for a count time series model based on a Gaussian or Student–t copula using the Continuous Extension (CE) method.

Usage

pmvn_ce(lower, upper, tau, od, c = 0.5, ret_llk = TRUE)

pmvt_ce(lower, upper, tau, od, c = 0.5, ret_llk = TRUE, df)

Arguments

Details

The CE method replaces the discrete probability mass at each observation with a smooth approximation controlled by a bandwidth parameter c. This yields a tractable approximation to the multivariate rectangle probability defining the likelihood.

Two copula families are supported:

• Gaussian copula via pmvn_ce()

• t copula via pmvt_ce()

In both cases, the latent dependence structure is specified through an ARMA(p,q) model.

The CE approximation applies to discrete marginal distributions once the corresponding latent lower and upper bounds are computed. The Gaussian copula version uses the standard normal cdf, while the t copula version uses the Student t cdf with degrees of freedom df.

Value

A numeric value giving the approximate log-likelihood.

References

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.

See Also

pmvn_ce, pmvt_ce

Examples

## Gaussian copula example
mu <- 10
tau <- 0.2
arma_order <- c(1, 0)

sim_data <- sim_poisson(mu = mu, tau = tau, arma_order = arma_order, 
                        nsim = 500, family = "gaussian", seed = 1)

y <- sim_data$y
a <- qnorm(ppois(y - 1, lambda = mu))
b <- qnorm(ppois(y, lambda = mu))

llk_gauss <- pmvn_ce(lower = a, upper = b,
                     tau = tau, od = arma_order, c = 0.5)


## t copula example
df <- 8

sim_data_t <- sim_poisson(mu = mu, tau = tau, arma_order = arma_order,
                          nsim = 500, family = "t", df = df, seed = 1)

y_t <- sim_data_t$y
a_t <- qt(ppois(y_t - 1, lambda = mu), df = df)
b_t <- qt(ppois(y_t, lambda = mu), df = df)

llk_t <- pmvt_ce(lower = a_t, upper = b_t, tau = tau, od = arma_order,
                 c = 0.5, df = df)

Approximate Log-Likelihood via GHK Simulation

Description

Computes the approximate log-likelihood for a count time series model based on a Gaussian or Student–t copula using the Geweke–Hajivassiliou–Keane (GHK) simulator.

Usage

pmvn_ghk(lower, upper, tau, od, M = 1000, QMC = TRUE, ret_llk = TRUE)

pmvt_ghk(
  lower,
  upper,
  tau,
  od,
  M = 1000,
  QMC = TRUE,
  ret_llk = TRUE,
  df,
  engine = c("mvmn", "mvt")
)

Arguments

Details

The GHK method approximates the multivariate normal or Student–t rectangle probability defining the copula likelihood by sequential simulation from truncated conditional distributions.

Two copula families are supported:

• Gaussian copula via pmvn_ghk()

• Student–t copula via pmvt_ghk()

In both cases, the latent dependence structure is parameterized through an ARMA(p,q) process.

The GHK simulator approximates the multivariate normal or t rectangle probability by decomposing it into a sequence of one-dimensional truncated conditional distributions.

Value

By default, a numeric scalar giving the approximate log-likelihood. If ret_llk = FALSE, internal diagnostic quantities from the GHK simulator are returned (primarily for internal use).

References

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

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

See Also

pmvn_ghk, pmvt_ghk

Examples

## Gaussian copula example
mu <- 10
tau <- 0.2
arma_order <- c(1, 0)

sim_data <- sim_poisson(mu = mu, tau = tau, arma_order = arma_order,
                        nsim = 500, family = "gaussian", seed = 1)

y <- sim_data$y
a <- qnorm(ppois(y - 1, lambda = mu))
b <- qnorm(ppois(y, lambda = mu))

llk_gauss <- pmvn_ghk(lower = a, upper = b, tau = tau, od = arma_order,
                      M = 1000)


## Student--t copula example
df <- 8

sim_data_t <- sim_poisson(mu = mu, tau = tau, arma_order = arma_order,
                          nsim = 500, family = "t", df = df, seed = 1)

y_t <- sim_data_t$y
a_t <- qt(ppois(y_t - 1, lambda = mu), df = df)
b_t <- qt(ppois(y_t, lambda = mu), df = df)

llk_t <- pmvt_ghk(lower = a_t, upper = b_t, tau = tau, od = arma_order,
                  M = 1000, df = df)

Approximate Log-Likelihood via TMET

Description

Computes the approximate log-likelihood for a count time series model based on a Gaussian and Student –t copula using the Time Series Minimax Exponential Tilting (TMET) method.

Usage

pmvn_tmet(lower, upper, tau, od, pm = 30, M = 1000, QMC = TRUE, ret_llk = TRUE)

pmvt_tmet(
  lower,
  upper,
  tau,
  od,
  pm = 30,
  M = 1000,
  QMC = TRUE,
  ret_llk = TRUE,
  df
)

Arguments

Details

TMET exploits the autoregressive moving-average (ARMA) structure of the latent Gaussian or Scale mixture normal representation of Student–t process to evaluate high-dimensional multivariate normal/t rectangle probabilities via adaptive importance sampling with an optimal tilting parameter.

The implementation combines the Innovations Algorithm for exact conditional mean and variance computation with exponential tilting, resulting in a scalable and variance-efficient likelihood approximation.

In this package, the latent dependence structure is parameterized through an ARMA(p,q) process.

Value

A numeric scalar giving the approximate log-likelihood. If ret_llk = FALSE, diagnostic output from the TMET sampler is returned (primarily for research use).

References

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

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

See Also

pmvn_ghk, pmvt_ghk

Examples

## Gaussian copula example
mu <- 10
tau <- 0.2
arma_order <- c(1, 0)

sim_data <- sim_poisson(mu = mu, tau = tau, arma_order = arma_order,
                        nsim = 1000, seed = 1)

y <- sim_data$y
a <- qnorm(ppois(y - 1, lambda = mu))
b <- qnorm(ppois(y, lambda = mu))

# Approximate log-likelihood using TMET
llk_tmet <- pmvn_tmet(lower = a, upper = b,
                      tau = tau, od = arma_order)
llk_tmet

## Student--t copula example
df <- 8

sim_data_t <- sim_poisson(mu = mu, tau = tau, arma_order = arma_order,
                          nsim = 500, family = "t", df = df, seed = 1)

y_t <- sim_data_t$y
a_t <- qt(ppois(y_t - 1, lambda = mu), df = df)
b_t <- qt(ppois(y_t, lambda = mu), df = df)

llk_t <- pmvt_tmet(lower = a_t, upper = b_t, tau = tau, od = arma_order,
                  M = 1000, df = df)
                  

One-Step-Ahead Predictive Distribution for Copula Count Time Series Models

Description

Computes the one-step-ahead predictive distribution for a fitted Gaussian or Student–t copula count time series model.

The predictive probability mass function is evaluated using the estimation method stored in the fitted object (TMET or GHK). Summary statistics of the predictive distribution are returned, and optional scoring rules are computed if the observed value is supplied.

Usage

## S3 method for class 'gctsc'
predict(object, y_obs = NULL, X_test = NULL, ...)

Arguments

Details

The predictive distribution integrates over the latent copula dependence structure specified in the fitted model. For Gaussian copulas, multivariate normal rectangle probabilities are evaluated; for Student–t copulas, multivariate t rectangle probabilities are used.

Value

A list containing:

• mean: Predictive mean.

• median: Predictive median.

• mode: Predictive mode.

• variance: Predictive variance.

• p_y: Predictive probability mass function over 0:y_max.

• lower, upper: Bounds of the 95\

• CRPS: Continuous Ranked Probability Score (if y_obs is provided).

• LOGS: Logarithmic Score (if y_obs is provided).

References

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

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

See Also

gctsc, arma.cormat

Examples

# Simulate Poisson AR(1) data
set.seed(1)
y_sim <- sim_poisson(mu = 10, tau = 0.2,
                     arma_order = c(1, 0),
                     nsim = 1000,
                     family = "gaussian")$y

# Fit Gaussian copula model
fit <- gctsc(
  y ~ 1,
  data = data.frame(y = y_sim),
  marginal = poisson.marg(lambda.lower = 0),
  cormat = arma.cormat(p = 1, q = 0),
  method = "CE",
  family = "gaussian",
  options = gctsc.opts(M = 1000, seed = 42)
)

# One-step-ahead prediction
predict(fit)

Print a gctsc Model Object

Description

Displays the call, estimation method, parameter estimates, and likelihood information.

Usage

## S3 method for class 'gctsc'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Print Summary of a gctsc Model

Description

Displays summary statistics and model fit information for a fitted gctsc model.

Usage

## S3 method for class 'summary.gctsc'
print(x, digits = 4, ...)

Arguments

Randomized Quantile Residuals for Copula Count Time Series Models

Description

Computes randomized quantile residuals for a fitted Gaussian or Student–t copula count time series model.

For discrete responses, residuals are constructed using the randomized probability integral transform (PIT) as proposed by Dunn and Smyth (1996). When the likelihood is evaluated via simulation (TMET or GHK), the same engine is used to approximate the required conditional probabilities.

Usage

## S3 method for class 'gctsc'
residuals(object, ...)

Arguments

Details

For observation y_t, let F_t(y_t^-) and F_t(y_t) denote the conditional CDF evaluated at y_t - 1 and y_t, respectively. The PIT value is computed as

e_t = F_t(y_t^-) + u_t \{F_t(y_t) - F_t(y_t^-)\},

where u_t \sim \mathrm{Uniform}(0,1).

For Gaussian copulas, residuals are obtained as r_t = \Phi^{-1}(e_t).

For Student–t copulas with degrees of freedom df, the residuals are defined as r_t = t_{\nu}^{-1}(e_t), where t_{\nu}^{-1} denotes the quantile function of the Student–t distribution.

Value

A list of class "gctsc.residuals" containing:

• residuals: Numeric vector of randomized quantile residuals.

• pit: Numeric vector of probability integral transform values.

References

Dunn, P. K. and Smyth, G. K. (1996), Randomized quantile residuals, Journal of Computational and Graphical Statistics, 5(3): 236–244.

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.

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

Examples

# Simulate Poisson AR(1) data under a Gaussian copula
set.seed(1)
y <- sim_poisson(mu = 5, tau = 0.7,
                 arma_order = c(1, 0),
                 nsim = 500,
                 family = "gaussian")$y

fit <- gctsc(
  y ~ 1,
  data = data.frame(y = y),
  marginal = poisson.marg(),
  cormat = arma.cormat(1, 0),
  family = "gaussian",
  method = "CE",
  options = gctsc.opts(seed = 1, M = 1000)
)

res <- residuals(fit)
hist(res$residuals, main = "Randomized Quantile Residuals")
hist(res$pit, main = "PIT Histogram")

Weekly Rotavirus case counts across Germany

Description

Weekly Rotavirus case counts across Germany

Usage

data("rota")

Format

A data frame with 1248 rows and 413 variables.

Simulate from Gaussian and t Copula Time Series Models

Description

These functions simulate time series data from Gaussian and t copula models with various discrete marginals and an ARMA dependence structure.

Usage

sim_poisson(
  mu,
  tau,
  arma_order,
  nsim,
  family = c("gaussian", "t"),
  df = NULL,
  seed = NULL
)

sim_negbin(
  mu,
  dispersion,
  tau,
  arma_order,
  nsim = 100,
  family = c("gaussian", "t"),
  df = NULL,
  seed = NULL
)

sim_zip(
  mu,
  pi0,
  tau,
  arma_order,
  nsim = 100,
  family = c("gaussian", "t"),
  df = NULL,
  seed = NULL
)

sim_binom(
  prob,
  size,
  tau,
  arma_order,
  nsim = 100,
  family = c("gaussian", "t"),
  df = NULL,
  seed = NULL
)

sim_bbinom(
  prob,
  rho,
  size,
  tau,
  arma_order,
  nsim = 100,
  family = c("gaussian", "t"),
  df = NULL,
  seed = NULL
)

sim_zib(
  prob,
  pi0,
  size,
  tau,
  arma_order,
  nsim = 100,
  family = c("gaussian", "t"),
  df = NULL,
  seed = NULL
)

sim_zibb(
  prob,
  rho,
  pi0,
  size,
  tau,
  arma_order,
  nsim = 100,
  family = c("gaussian", "t"),
  df = NULL,
  seed = NULL
)

Arguments

Details

Marginal types:

• Poisson: Counts with mean \mu.

• Negative binomial (NB): Overdispersed counts with mean \mu and dispersion parameter \kappa.

• Binomial: Number of successes in n trials with success probability p.

• Beta–-binomial (BB): Binomial with success probability p following a beta distribution, allowing intra-cluster correlation \rho.

• Zero–inflated Poisson (ZIP): Poisson with extra probability \pi_0 of an excess zero.

• Zero–inflated binomial (ZIB): Binomial with extra probability \pi_0 of an excess zero.

• Zero–inflated beta–binomial (ZIBB): Beta–binomial with extra probability \pi_0 of an excess zero.

Parameterization notes:

• Negative binomial uses dispersion (\kappa) to model overdispersion: larger dispersion increases variance for a fixed mean.

• Beta–binomial and ZIBB use rho as the overdispersion parameter: \rho is the intra-class correlation, with \rho \to 0 giving the binomial model.

• Zero–inflated marginals include a separate pi0 parameter that controls the extra probability mass at zero.

Value

A list with components:

• y: Simulated time series data.

• z: Latent Gaussian process values.

• marginal: Marginal distribution name.

• parameters: List of parameters used.

• cormat: ARMA structure.

Examples

# Poisson example
sim_poisson(mu = 10, tau = c(0.2, 0.2), 
  arma_order = c(1, 1), nsim = 100, 
  family = "gaussian", seed = 42)

# Negative Binomial example
sim_negbin(mu = 10, dispersion = 2, tau = c(0.5, 0.5),
  arma_order = c(1, 1),family = "gaussian",
  nsim = 100, seed =1)

# Zero Inflated Beta-Binomial example with seasonal covariates
n <- 100
xi <- numeric(n)
zeta <- rnorm(n)
for (j in 3:n) {
  xi[j] <- 0.6 * xi[j - 1] - 0.4 * xi[j - 2] + zeta[j]
}
prob <- plogis(0.2 + 0.3 * sin(2 * pi * (1:n) / 12) +
             0.5 * cos(2 * pi * (1:n) / 12) + 0.3 * xi)
sim_zibb(prob, rho = 1/6, pi0 = 0.2, size = 24, tau = 0.5,
 arma_order = c(1, 0),family = "t", df = 10, nsim = 100)

Summarize a gctsc Model Fit

Description

Computes standard errors, z-values, and p-values for the estimated parameters in a fitted gctsc object.

Usage

## S3 method for class 'gctsc'
summary(object, ...)

Arguments

Value

A list of class summary.gctsc containing model summary statistics.