fport_gof: Goodness-of-fit Tests for Functional Times Series

In FTSgof: White Noise and Goodness-of-Fit Tests for Functional Time Series

Goodness-of-fit Tests for Functional Times Series

Description

It computes three different goodness-of-fit tests for functional time series. All goodness-of-fit tests in this package are accessible through this function.

Usage

fport_gof(
  f_data,
  test = "far",
  H = 10,
  M = NULL,
  pplot = FALSE,
  residual = 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.
test	A string specifying the goodness-of-fit test. Currently available tests are referred to by their string handles: "far", "arch" and "garch". Please see the Details section of the documentation.
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 in the "far" test, and the number of basis functions used in the "arch" and "garch" tests. If M = NULL, then for the "far" test, M is calculated as \text{floor}((\max(150 - N, 0) + \max(100 - J, 0) + (J / \sqrt{2}))), ensuring the number of Monte Carlo simulations is adequate based on the dataset size. For the "arch" or "garch" test, M is set to 1.
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.

Details

This function conducts goodness-of-fit tests for functional time series data, providing several testing options:

1. When test = "far", it tests the goodness-of-fit of the FAR(1) model. The function fits the FAR(1) model to the input data and then applies the test statistic KRS_{N,H}, as described in fport_wn, to the residuals. The null distribution of the test statistic accounts for the dependence structure present in the residuals. The optional parameters for this test are 'fdata', 'test', 'H', 'M', 'pplot' and 'residual'.

2. When test = "arch" or "garch", it tests the goodness-of-fit of the fARCH(1) or fGARCH(1,1) models. It fits the model to the input data and applies the test M_{N,H} in fport_wn to the model residuals. The asymptotic distribution is adjusted to account for the estimation effect, because the model residual depends on the joint asymptotics of the innovation process and the estimated parameters. We assume that the kernel parameters are consistently estimated by the Least Squares method proposed in Aue et al. (2017). Then, the asymptotic distribution of the statistic M_{N,H} is given in Theorem 3.1 in Rice et al. (2020). The optional parameters for this test are 'fdata', 'test', 'H', 'M', and 'pplot'.

Value

A summary is printed with a brief explanation of the test and the p-value.

References

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

[2] Aue, A., Horvath, L., F. Pellatt, D. (2017). Functional generalized autoregressive conditional heteroskedasticity. Journal of Time Series Analysis. 38(1), 3-21. <doi:10.1111/jtsa.12192>.

[3] Rice, G., Wirjanto, T., Zhao, Y. (2020). Tests for conditional heteroscedasticity of functional data. Journal of Time Series Analysis. 41(6), 733-758. <doi:10.1111/jtsa.12532>.

Examples

data(Spanish_elec)
fport_gof(Spanish_elec, test = "far", H = 20, pplot=TRUE)

data(sp500)
fport_gof(OCIDR(sp500), test = "arch", M = 1, H = 5)
fport_gof(OCIDR(sp500), test = "garch", M = 1, H = 10)

FTSgof documentation built on Oct. 4, 2024, 1:06 a.m.