fACF_test {FTSgof} | R Documentation |
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 |
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 |
pplot |
A Boolean value. If TRUE, the function will produce a plot of p-values of the test
as a function of maximum lag |
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)