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
)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.
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.
A positive integer specifying the maximum lag for which test statistic is computed.
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.
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.
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.
A numeric value between 0 and 1 indicating the significance level for the test.
A Boolean value. If TRUE, the function will not return the list containing the p-value, quantile, and statistic.
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.
[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.
# \donttest{
data(sp500) # S&P500 index
fACF_test(OCIDR(sp500), H = 10, pplot=TRUE)
# }
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