A recursive algorithm for detecting and locating multiple variance
change points in a sequence of random variables with long-range
dependence.
Usage
testing.hov(x, wf, J, min.coef=128, debug=FALSE)
Arguments
x
Sequence of observations from a (long memory) time series.
wf
Name of the wavelet filter to use in the decomposition.
J
Specifies the depth of the decomposition. This must be a number
less than or equal to
$\log(\mbox{length}(x),2)$.
min.coef
Minimum number of wavelet coefficients for testing purposes.
Empirical results suggest that 128 is a reasonable number in order
to apply asymptotic critical values.
debug
Boolean variable: if set to TRUE, actions taken by
the algorithm are printed to the screen.
Value
Matrix whose columns include (1) the level of the wavelet transform
where the variance change occurs, (2) the value of the test statistic,
(3) the DWT coefficient where the change point is located, (4) the
MODWT coefficient where the change point is located. Note, there is
currently no checking that the MODWT is contained within the
associated support of the DWT coefficient. This could lead to
incorrect estimates of the location of the variance change.
Details
For details see Section 9.6 of Percival and Walden (2000) or Section
7.3 in Gencay, Selcuk and Whitcher (2001).
References
Gencay, R., F. Selcuk and B. Whitcher (2001)
An Introduction to Wavelets and Other Filtering Methods in
Finance and Economics,
Academic Press.
Percival, D. B. and A. T. Walden (2000)
Wavelet Methods for Time Series Analysis,
Cambridge University Press.