FTSgof (version 1.0.0)

gof_far: Goodness-of-fit test for FAR(1)

Description

It fits a FAR(1) model and then assesses the cumulative significance of lagged autocovariance operators from the model residuals, up to a user-selected maximum lag \(H\).

Usage

gof_far(
  f_data,
  H = 10,
  M = NULL,
  alpha = 0.05,
  pplot = FALSE,
  residual = FALSE,
  suppress_raw_output = FALSE,
  suppress_print_output = FALSE
)

Value

If suppress_raw_output = FALSE, a list containing the test statistic, the \((1-\alpha)\) quantile of the limiting distribution, and the p-value computed from the specified hypothesis test. Also prints output containing a short description of the test, the p-value, and additional information about the test if suppress_print_output = FALSE.

Arguments

f_data

A \(J \times N\) matrix of functional time series data, where \(J\) is the number of discrete points in a grid and \(N\) is the sample size.

H

A positive integer specifying the maximum lag for which test statistics are computed.

M

A positive integer specifying the number of Monte Carlo simulations used to approximate the null distribution. If \(M = NULL, M = \text{floor}((\max(150 - N, 0) + \max(100 - J, 0) + (J / \sqrt{2})))\), ensuring that the number of Monte Carlo simulations is adequate based on the dataset size.

alpha

A numeric value between 0 and 1 specifying the significance level.

pplot

A Boolean value. If TRUE, the function will produce a plot of p-values of the test as a function of maximum lag \(H\), ranging from \(H=1\) to \(H=20\), which may increase the computation time.

residual

A data frame. If TRUE, the function will provide the residuals obtained from fitting the FAR(1) model.

suppress_raw_output

A Boolean value, FALSE by default. If TRUE, the function will not return the list containing the p-value, quantile, and statistic.

suppress_print_output

A Boolean value, FALSE by default. If TRUE, the function will not print any output to the console.

References

[1] Kim, M., Kokoszka, P., & Rice, G. (2023). White noise testing for functional time series. Statistic Surveys, 17, 119-168.

Examples

# \donttest{
yd_far <- dgp.far(J=50, N=100, S=0.7, p=2, kernel = "Gaussian", burn_in = 50)
gof_far(yd_far, H=5, pplot=TRUE)
# }