est_cfarh {NTS}

Estimation of a CFAR Process with Heteroscedasticity and Irregualar Observation Locations

Description

Estimation of a CFAR process with heteroscedasticity and irregualar observation locations.

Usage

est_cfarh(
  f,
  weight,
  p = 2,
  grid = 1000,
  df_b = 5,
  num_obs = NULL,
  x_pos = NULL
)

Arguments

f

the functional time series.

weight

the covariance functions of noise process.

p

the CFAR order.

grid

the number of gird points used to construct the functional time series and noise process. Default is 1000.

df_b

the degrees of freedom for natural cubic splines. Default is 10.

num_obs

the numbers of observations. It is a t-by-1 vector, where t is the length of time.

x_pos

the observation location matrix. If the locations are regular, it is a t-by-(n+1) matrix with all entries 1/n.

Value

The function returns a list with components:

phi_coef

the estimated spline coefficients for convolutional function(s).

phi_func

the estimated convolutional function(s).

rho

estimated rho for O-U process (noise process).

sigma

estimated sigma for O-U process (noise process).

References

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