g_cfar2h function

Generate a CFAR(2) Process with Heteroscedasticity and Irregular Observation Locations

Generate a convolutional functional autoregressive process of order 2 with heteroscedasticity, irregular observation locations.

g_cfar2h(
  tmax = 1001,
  grid = 1000,
  rho = 1,
  min_obs = 40,
  pois = 5,
  phi_func1 = NULL,
  phi_func2 = NULL,
  weight = NULL,
  ini = 100
)

Arguments

• tmax: length of time.
• grid: the number of grid points used to construct the functional time series.
• rho: parameter for O-U process (noise process).
• min_obs: the minimum number of observations at each time.
• pois: the mean for Poisson distribution. The number of observations at each follows a Poisson distribution plus min_obs.
• phi_func1: the first convolutional function. Default is 0.5x^2+0.5x+0.13.
• phi_func2: the second convolutional function. Default is 0.7x^4-0.1x^3-0.15*x.
• weight: the weight function to determine the standard deviation of O-U process (noise process). Default is 1.
• ini: the burn-in period.

Returns

The function returns a list with components: - cfar2: a tmax-by-(grid+1) matrix following a CFAR(1) process.

• epsilon: the innovation at time tmax.

Examples

phi_func1= function(x){
return(0.5*x^2+0.5*x+0.13)
}
phi_func2= function(x){
return(0.7*x^4-0.1*x^3-0.15*x)
}
y=g_cfar2h(200,1000,1,40,5,phi_func1=phi_func1,phi_func2=phi_func2)

References

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