single_lag_test {wwntests}

Single-Lag Hypothesis Test

Description

'single_lag_test' computes the single-lag hypothesis test at a single user-specified lag.

Usage

single_lag_test(
  f_data,
  lag = 1,
  alpha = 0.05,
  iid = FALSE,
  M = NULL,
  bootstrap = FALSE,
  block_size = "adaptive",
  straps = 300,
  moving = FALSE,
  suppress_raw_output = FALSE,
  suppress_print_output = FALSE
)

Arguments

f_data

The functional data matrix with observed functions in the columns

lag

Positive integer value. The lag to use to compute the single lag test statistic.

alpha

Numeric value between 0 and 1 specifying the significance level to be used in the specified hypothesis test. The default value is 0.05. Note, the significance value is only ever used to compute the 1-alpha quantile of the limiting distribution of the specified test's test statistic.

iid

A Boolean value, FALSE by default. If given TRUE, the hypothesis test will use a strong-white noise assumption (instead of a weak-white noise assumption).

M

Positive integer value. Number of Monte-Carlo simulations for the Welch-Satterthwaite approximation.

bootstrap

A Boolean value, FALSE by default. If given TRUE, the hypothesis test is done by approximating the limiting distribution of the test statistic via a block bootstrap process.

block_size

A positive Integer value, with the default value being computed via the adaptive bandwidth selection method in the "spectral" test. Determines the block size (of each block in each bootstrap sample) if the test is being bootstrapped.

straps

A positive Integer, with a default value of 300. Determines the number of bootstrap samples to take if the test is being bootstrapped. Only used if 'bootstrap' == TRUE.

moving

A Boolean value, FALSE by default. If given TRUE, the performed block bootstrap will be moving rather than stationary.

suppress_raw_output

Boolean value, FALSE by default. If TRUE, the function will not return the list containing the p-value, quantile, and statistic.

suppress_print_output

Boolean value, FALSE by default. If TRUE, the function will not print any output to the console.

Details

The "single-lag" portmanteau test is based on the sample autocovariance function computed from the functional data. This test assesses the significance of lagged autocovariance operators at a single, user-specified lag h. More specifically, it tests the null hypothesis that the lag-h autocovariance operator is equal to 0. This test is designed for stationary functional time-series, and is valid under conditional heteroscedasticity conditions.

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] 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

f <- far_1_S(150, 50, S = 0.75)
single_lag_test(f, lag = 1)
single_lag_test(f, lag = 2, M=100)