g_cfar1 function

Generate a CFAR(1) Process

Generate a convolutional functional autoregressive process with order 1.

g_cfar1(
  tmax = 1001,
  rho = 5,
  phi_func = NULL,
  grid = 1000,
  sigma = 1,
  ini = 100
)

Arguments

• tmax: length of time.
• rho: parameter for O-U process (noise process).
• phi_func: convolutional function. Default is density function of normal distribution with mean 0 and standard deviation 0.1.
• grid: the number of grid points used to construct the functional time series. Default is 1000.
• sigma: the standard deviation of O-U process. Default is 1.
• ini: the burn-in period.

Returns

The function returns a list with components: - cfar1: a tmax-by-(grid+1) matrix following a CFAR(1) process.

• epsilon: the innovation at time tmax.

Examples

phi_func= function(x)
{
        return(dnorm(x,mean=0,sd=0.1))
}
y=g_cfar1(100,5,phi_func,grid=1000,sigma=1,ini=100)

References

Liu, X., Xiao, H., and Chen, R. (2016) Convolutional autoregressive models for functional time series. Journal of Econometrics, 194, 263-282.