fSACF_test: Test based on fSACF

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

Test based on fSACF

Description

This function performs a hypothesis test using a test statistic computed from functional spherical autocorrelation coefficients of a FTS.

Usage

fSACF_test(
  f_data,
  H = 10,
  alpha = 0.05,
  pplot = FALSE,
  suppress_raw_output = FALSE,
  suppress_print_output = FALSE
)

Arguments

f_data	A J \times N matrix of functional time series data, where J represents the number of discrete points in a grid and N represents the sample size.
H	A positive integer specifying the maximum lag for which test statistic is computed.
alpha	A numeric value between 0 and 1 indicating the significance level for the test.
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.
suppress_raw_output	A Boolean value. If TRUE, the function will not return the list containing the p-value, quantile, and statistic.
suppress_print_output	A Boolean value. If TRUE, the function will not print any output to the console.

Details

The test statistic is the sum of the squared L^2-norm of the sample spherical autocorrelation coefficients:

S_{N,H} = N \sum_{h=1}^H \|\tilde{\rho}_{h}\|^2,

where \tilde\rho_h=\frac{1}{N}\sum_{i=1}^{N-h} \langle \frac{X_i - \tilde{\mu}}{\|X_i - \tilde{\mu}\|}, \frac{X_{i+h} - \tilde{\mu}}{\|X_{i+h} - \tilde{\mu}\|} \rangle, and \tilde{\mu} is the estimated spatial median of the series. This test assesses the cumulative significance of lagged spherical autocorrelation coefficients, up to a user-selected maximum lag H. A higher value of S_{N,H} suggests a potential departure of the observed series from white noise process. The approximated null distribution of this statistic is developed under the strong white noise assumptions.

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.

References

[1] Yeh CK, Rice G, Dubin JA (2023). “Functional spherical autocorrelation: A robust estimate of the autocorrelation of a functional time series.” Electronic Journal of Statistics, 17, 650–687.

Examples

data(Spanish_elec)
fACF_test(Spanish_elec, H = 20)

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