Simulate Data from a Vector Autoregressive Zero-Inflated Poisson (VARZIP) Model

This function generates synthetic time series data from a Vector Autoregressive Zero-Inflated Poisson (VARZIP) model.

Usage

SimVARZIP(time, burn_in, constant, coef, chol_cov)

Arguments

time

Integer. Number of time points to simulate.

burn_in

Integer. Number of burn-in observations to exclude before returning the results.

constant

Numeric vector. The constant term vector of length k, where k is the number of variables.

coef

Numeric matrix. Coefficient matrix with dimensions k by (k * p). Each k by k block corresponds to the coefficient matrix for a particular lag.

chol_cov

Numeric matrix. The Cholesky decomposition of the covariance matrix of the multivariate normal noise. It should have dimensions k by k.

Value

Numeric matrix containing the simulated time series data with dimensions k by time, where k is the number of variables and time is the number of observations.

Details

The SimVARZIP() function generates synthetic time series data from a Vector Autoregressive (VAR) with Zero-Inflated Poisson (ZIP) model for the first observed variable. See SimVAR() for more details on generating data for VAR(p). The SimVARZIP function goes further by using the generated values for the first variable to generate data from the ZIP model. The exponential of the values from the first variable from the original VAR(p) model are used as the intensity parameter in the Poisson distribution in the ZIP model. Data from the ZIP model are used to replace the original values for the first variable. Values for the rest of the variables are unchanged. The generated data includes a burn-in period, which is excluded before returning the results.

The steps involved in generating the time series data are as follows:

• Extract the number of variables k and the number of lags p from the input.

• Create a matrix data of size k x (time + burn_in) to store the generated data.

• Set the initial values of the matrix data using the constant term constant.

• For each time point starting from the p-th time point to time + burn_in - 1:

  • Generate a vector of random process noise from a multivariate normal distribution with mean 0 and covariance matrix chol_cov.

  • Generate the VAR time series values for each variable j at time t by applying the autoregressive terms for each lag lag and each variable l.

    • Add the generated noise to the VAR time series values.

    • For the first variable, apply the Zero-Inflated Poisson (ZIP) model:

      • Compute the intensity intensity as the exponential of the first variable's value at time t.

      • Sample a random value u from a uniform distribution on [0, 1].

      • If u is less than intensity / (1 + intensity), set the first variable's value to zero (inflation).

      • Otherwise, sample the first variable's value from a Poisson distribution with mean intensity (count process).

• Transpose the data matrix data and return only the required time period after burn-in as a numeric matrix.

See also

Other Simulation of Autoregressive Data Functions: CheckARCoef(), CheckVARCoef(), SimARCoef(), SimAR(), SimMVN(), SimPD(), SimVARCoef(), SimVARExo(), SimVARZIPExo(), SimVAR(), SimVariance(), YXExo(), YX()

Author

Ivan Jacob Agaloos Pesigan

Examples

set.seed(42)
time <- 50L
burn_in <- 10L
k <- 3
p <- 2
constant <- c(1, 1, 1)
coef <- matrix(
  data = c(
    0.4, 0.0, 0.0, 0.1, 0.0, 0.0,
    0.0, 0.5, 0.0, 0.0, 0.2, 0.0,
    0.0, 0.0, 0.6, 0.0, 0.0, 0.3
  ),
  nrow = k,
  byrow = TRUE
)
chol_cov <- chol(diag(3))
y <- SimVARZIP(
  time = time,
  burn_in = burn_in,
  constant = constant,
  coef = coef,
  chol_cov = chol_cov
)
head(y)
#>      [,1]     [,2]     [,3]
#> [1,]    0 3.271626 4.772946
#> [2,]    0 3.297536 5.918128
#> [3,]    1 2.039249 4.670999
#> [4,]    0 3.177612 3.249752
#> [5,]    0 4.138388 2.583101
#> [6,]    2 4.479106 4.351911