fACF_test | R Documentation |
This function performs a hypothesis test using a test statistic computed from functional autocovariance kernels of a FTS.
fACF_test(
f_data,
H = 10,
iid = FALSE,
M = NULL,
pplot = FALSE,
alpha = 0.05,
suppress_raw_output = FALSE,
suppress_print_output = FALSE
)
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. |
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.
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.
[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.
data(sp500) # S&P500 index
fACF_test(OCIDR(sp500), H = 10, pplot=TRUE)
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