independence_test {wwntests}

Independence Test

Description

'independence_test' Computes the independence test with a user-specified number of principal components and range of lags.

Usage

independence_test(
  f_data,
  components,
  lag,
  alpha = 0.05,
  suppress_raw_output = FALSE,
  suppress_print_output = FALSE
)

Arguments

f_data

The functional data matrix with observed functions in the columns

components

A positive Integer specifying the number of principal components to project the data on; ranked in order of importance (importance is determined by the proportion of the variance that is explained by the individual principal component.)

lag

A positive Integer value, specifying the maximum lag to include - this can be seen as the bandwidth or lag-window.

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 "independence" portmanteau test is a test of independence and identical distribution based on a dimensionality reduction by projecting the data onto the most important functional principal components. It is based on the resulting lagged cross-variances. This test is not for general white noise series, and may not hold under functional conditionally heteroscedastic assumptions. Please consult the vignette for a deeper exposition, and consult the reference for a complete treatment.

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] Gabrys R., & Kokoszka P. (2007). Portmanteau Test of Independence for Functional Observations. Journal of the American Statistical Association, 102:480, 1338-1348, DOI: 10.1198/016214507000001111.

Examples

b <- brown_motion(250, 100)
independence_test(b, components = 3, lag = 5)