hwwntest-package {hwwntest}

Tests of White Noise using Wavelets

Description

Provides methods to test whether time series is consistent with white noise. Two new tests based on Haar wavelets and general wavelets described by Nason and Savchev (2014) <doi:10.1002/sta4.69> are provided and, for comparison purposes this package also implements the B test of Bartlett (1967) <doi:10.2307/2333850>. Functionality is provided to compute an approximation to the theoretical power of the general wavelet test in the case of general ARMA alternatives.

Details

The DESCRIPTION file:

Package:	hwwntest
Type:	Package
Title:	Tests of White Noise using Wavelets
Version:	1.3.2
Date:	2023-09-06
Authors@R:	c(person("Delyan", "Savchev", role=c("aut"),email="[e-mail]"), person("Guy", "Nason", role=c("aut","cre"), email="[e-mail]"))
Description:	Provides methods to test whether time series is consistent with white noise. Two new tests based on Haar wavelets and general wavelets described by Nason and Savchev (2014) <doi:10.1002/sta4.69> are provided and, for comparison purposes this package also implements the B test of Bartlett (1967) <doi:10.2307/2333850>. Functionality is provided to compute an approximation to the theoretical power of the general wavelet test in the case of general ARMA alternatives.
Depends:	R(>= 3.3)
Imports:	parallel, polynom, wavethresh
License:	GPL-2
Author:	Delyan Savchev [aut], Guy Nason [aut, cre]
Maintainer:	Guy Nason <[e-mail]>

Index of help topics:

Macdonald               Compute the Macdonald density function for a
                        specified parameter value 'm' at a vector of
                        'x' values.
bartlettB.test          Bartlett's B test for white noise
compute.rejection       Function to compute empirical size or power for
                        various tests of white noise.
cumperiod               Compute cumulative normalized periodogram.
d00.test                Test for white noise based on the coarsest
                        scale Haar wavelet coefficient of the spectrum.
genwwn.powerplot        Plot (approximation) to the theoretical power
                        of the 'genwwn.test' test for ARMA processes
                        (including, of course, white noise itself) for
                        a range of sample sizes.
genwwn.test             White noise test using general wavelets.
genwwn.thpower          Compute (approximation) to the theoretical
                        power of the 'genwwn.test' test for ARMA
                        processes (including, of course, white noise
                        itself).
hwwn.dw                 Compute discrete wavelets
hwwn.test               Perform a test for white noise on a time
                        series.
hwwntest-package        Tests of White Noise using Wavelets
hywavwn.test            Hybrid wavelet test of white noise.
hywn.test               Hybrid of Box-Ljung test, Bartlett B test, Haar
                        wavelet and General wavelet tests.
sqcoefvec               Compute coefficients required for approximaing
                        the wavelet transform using the square of
                        wavelets.
sqndwd                  Compute the non-decimated squared wavelet
                        transform.
sqndwdecomp             Brute-force calculation of the non-decimated
                        squared wavelet transform.
sqwd                    Compute expansion with respect to squared
                        wavelets.

Contains a variety of hypothesis tests for white noise data. The package contains an implementation of Bartlett's B test, bartlettB.test, (Kolmogorov-Smirnov test on the cumulative periodogram), a selection of wavelet-based tests hwwn.test a test using Haar wavelets, d00.test a single Haar wavelet coefficient test, genwwn.test a test using smoother Daubechies wavelets, a hybrid test hywavwn.test that uses Haar wavelets at fine scales and general wavelets at coarse scales and a omnibus test hywn.test that combines the results of four tests (hwwn.test, genwwn.test, bartlettB.test and the Box.test) The wavelet tests work by examining the wavelet transform of the regular periodogram and assess whether it has non-zero coefficients. If series is H_0: white noise, then the underlying spectrum is constant (flat) and all true wavelet coefficients will be zero. Then all periodogram wavelet coefficients will have true zero mean which can be tested using knowledge of, or approximation to, the coefficient distribution.

Author(s)

NA

Maintainer: NA

References

Nason, G.P. and Savchev, D. (2014) White noise testing using wavelets. Stat, 3, 351-362. doi:10.1002/sta4.69

See Also

hwwn.test

Examples

 # Invent test data set which IS white noise
     #
     x <- rnorm(128)
     #
     # Do the test
     #
     x.wntest <- hwwn.test(x)
     #
     # Print the results
     #
     #x.wntest
     #
     #       Wavelet Test of White Noise
     #
     #data:
     #p-value = 0.9606
     #
     # So p-value indicates that there is no evidence for rejection of
     # H_0: white noise.
     #
     # Let's do an example using data that is not white noise. E.g. AR(1)
     #
     x.ar <- arima.sim(n=128, model=list(ar=0.8))
     #
     # Do the test
     #
     x.ar.wntest <- hwwn.test(x.ar)
     #
     # Print the results
     #
     print(x.ar.wntest)
     #
     #       Wavelet Test of White Noise
     #
     #data:
     #p-value < 2.2e-16
     #
     # p-value is very small. Extremely strong evidence
     # to reject H_0: white noise
     #
     #
     # Let's use one of the other tests: e.g. the general wavelet one
     #
     x.ar.genwwntest <- genwwn.test(x.ar)
     #
     # Print the results
     #
     print(x.ar.genwwntest)
     #
     #
     #  Wavelet Test of White Noise
     #
     # data:
     # p-value = 1.181e-10
     #
     # Again, p-value is very small