fACF_test: Test based on fACF

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

Test based on fACF

Description

This function performs a hypothesis test using a test statistic computed from functional autocovariance kernels of a FTS.

Usage

fACF_test(
  f_data,
  H = 10,
  iid = FALSE,
  M = NULL,
  pplot = FALSE,
  alpha = 0.05,
  suppress_raw_output = FALSE,
  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 statistic is computed.
iid	A Boolean value. If given TRUE, the hypothesis test will use the strong-white noise (SWN) assumption instead of the weak white noise (WWN) assumption.
M	A positive integer specifying the number of Monte Carlo simulations used to approximate the null distribution under the WWN assumption. 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.
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.
alpha	A numeric value between 0 and 1 indicating the significance level for the test.
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 autocovariance kernels:

KRS_{N,H} = N \sum_{h=1}^H \|\hat{\gamma}_{N,h}\|^2,

where \hat{\gamma}_{N,h}(t,s)=N^{-1}\sum_{i=1}^{N-h} (X_i(t)-\bar{X}_N(t))(X_{i+h}(s)-\bar{X}_N(s)), \bar{X}_N(t) = N^{-1} \sum_{i=1}^N X_i(t). This test assesses the cumulative significance of lagged autocovariance kernels, up to a user-selected maximum lag H. A higher value of KRS_{N,H} suggests a potential departure of the observed series from white noise process. The approximated null distribution of this statistic is developed under both the strong and weak white noise assumptions.

Value

If suppress_raw_output = FALSE, a list that includes the test statistic, the (1-\alpha) quantile of the limiting distribution, and the p-value from the specified hypothesis test. Additionally, if suppress_print_output = FALSE, a summary is printed with a brief explanation of the test, the p-value, and relevant details about the test procedure.

References

[1] Kokoszka P., Rice G., Shang H.L. (2017). Inference for the autocovariance of a functional time series under conditional heteroscedasticity. Journal of Multivariate Analysis, 162, 32-50.

Examples

data(sp500) # S&P500 index
fACF_test(OCIDR(sp500), H = 10, pplot=TRUE)

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