NTS (version 1.1.3)

g_cfar2h: Generate a CFAR(2) Process with Heteroscedasticity and Irregular Observation Locations

Description

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

Usage

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

Value

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.

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 0.5*x^2+0.5*x+0.13.

phi_func2

the second convolutional function. Default is 0.7*x^4-0.1*x^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.

References

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

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)