Skip to contents

Simulation of Count Time Series

Source: R/cocoSim.R
cocoSim.Rd

The function generates a time series of low counts from the (G)PAR model class for a specified innovation distribution, sample size, lag order, and parameter values.

Usage

cocoSim(
  type,
  order,
  par,
  length,
  xreg = NULL,
  init = NULL,
  julia = FALSE,
  julia_seed = NULL,
  link_function = "log"
)

Arguments

type

character, either "Poisson" or "GP" indicating the type of the innovation distribution

order

integer, either 1 or 2 indicating the order of the model

par

numeric vector, the parameters of the model, the number of elements in the vector depends on the type and order specified.

length

integer, the number of observations in the generated time series

xreg

data frame of control variables (defaul: NULL)

init

numeric vector, initial data to use (default: NULL). See details for more information on the usage.

julia

If TRUE, the julia implementation is used. In this case, init is ignored but it might be faster (default: FALSE).

julia_seed

Seed for the julia implementation. Only used if julia equals TRUE.

Specifies the link function for the conditional mean of the innovation (\(\lambda\)). The default is log, but other available options include identity and relu. This parameter is applicable only when covariates are used. Note that using the identity link function may result in \(\lambda\) becoming negative. To prevent this, ensure all covariates are positive and restrict the parameter \(\beta\) to positive values.

Value

a vector of the simulated time series

Details

The function checks for valid input of the type, order, parameters, and initial data before generating the time series.

The init parameter allows users to set a custom burn-in period for the simulation. By default, when simulating with covariates, no burn-in period is specified since there is no clear choice on the covariates. However, the init argument gives users the flexibility to select an appropriate burn-in period for the covariate case. One way to do this is to simulate a time series using cocoSim with appropriate covariates and pass the resulting time series to the init argument of a new cocoSim run so that the first time series is used as the burn-in period. If init is not specified for the covariate case, a warning will be returned to prompt the user to specify a custom burn-in period. This helps ensure that the simulation accurately captures the dynamics of the system being modeled.

Author

Manuel Huth

Examples

#First Order Model
lambda <- 1
alpha <- 0.4
set.seed(12345)

# Simulate using the RCPP implementation
data_rcpp <- cocoSim(order = 1, type = "Poisson", par = c(lambda, alpha), length = 100)

# Second Order Model
lambda <- 1
alpha_1 <- 0.3
alpha_2 <- 0.1
alpha_3 <- 0.2
eta <- 0.2
data_j <- cocoSim(order = 2, type = "GP",
                  par = c(lambda, alpha_1, alpha_2,alpha_3,eta),
                  length = 100)