Q_WS_hyp_test {wwntests}

Compute size alpha single-lag hypothesis test under weak or strong white noise assumption

Description

'Q_WS_hyp_test' computes the size alpha test of a single lag hypothesis under a weak white noise or strong white noise assumption using a Welch-Satterthwaite Approximation.

Usage

Q_WS_hyp_test(
  f_data,
  lag,
  alpha = 0.05,
  iid = FALSE,
  M = NULL,
  bootstrap = FALSE,
  block_size = "adaptive",
  straps = 300,
  moving = 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.

Value

A list containing the p-value, the quantile, and a boolean value indicating whether or not the hypothesis is rejected.