multi_lag_test {wwntests}

Multi-Lag Hypothesis Test

Description

'multi_lag_test' Computes the multi-lag hypothesis test over a range of user-specified lags.

Usage

multi_lag_test(
  f_data,
  lag = 20,
  M = NULL,
  iid = FALSE,
  alpha = 0.05,
  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 multi-lag test statistic

M

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

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).

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.

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 "multi-lag" portmanteau test is also based on the sample autocovariance function computed from the functional data. This test assesses the cumulative significance of lagged autocovariance operators, up to a user-selected maximum lag K. More specifically, it tests the null hypothesis that the first K lag-h autocovariance operators (h going from 1 to K) 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

b <- brown_motion(150, 50)
multi_lag_test(b, lag = 5)
multi_lag_test(b, lag = 10, M = 50)