spectral_test {wwntests}

Spectral Density Test

Description

The "spectral" portmanteau test is based on the spectral density operator. It essentially measures the proximity of a functional time series to a white noise - the constant spectral density operator of an uncorrelated series. Unlike the "single-lag" and "multi-lag" tests, this test is not for general white noise series, and may not hold under functional conditionally heteroscedastic assumptions.

Usage

spectral_test(
  f_data,
  kernel = "Bartlett",
  bandwidth = "adaptive",
  alpha = 0.05,
  suppress_raw_output = FALSE,
  suppress_print_output = FALSE
)

Arguments

f_data

The functional data matrix with observed functions in the columns

kernel

A String specifying the kernel function to use. The currently supported kernels are the 'Bartlett' and 'Parzen' kernels. The default kernel is 'Bartlett'.

bandwidth

A String or positive Integer value which specifies the bandwidth to use. Currently admitted string handles are 'static' which computes the bandwidth p via p = n^(1/(2q+1)) where n is the sample size and q is the kernel order, or 'adaptive' which uses a bandwidth selection method that is based on the functional data.

alpha

Numeric value between 0 and 1 specifying the significance level to be used for the test. The significance level is 0.05 by default. 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

'spectral_test' Computes the spectral hypothesis test under a user-specified kernel function and bandwidth; automatic bandwidth selection methods are provided.

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] Characiejus V., & Rice G. (2019). A general white noise test based on kernel lag-window estimates of the spectral density operator. Econometrics and Statistics, submitted.

[2] Chen W.W. & Deo R.S. (2004). Power transformations to induce normality and their applications. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66, 117–130.

Examples

b <- brown_motion(100, 50)
spectral_test(b)
spectral_test(b, kernel = 'Parzen', bandwidth = 'adaptive')
spectral_test(b, kernel = 'Bartlett', bandwidth = 2)