A vignette has been added, outlining the methods and working
through both example datasets. Open it with
vignette("QR-break", package = "QR.break").
rq.break(), sq(), dq(),
sq.test.0vs1(), dq.test.0vs1(),
sq.test.lvsl_1() and dq.test.lvsl_1() include
an optional argument norm.method, which selects how the
subgradient process underlying the SQ and DQ tests is normalized. The
argument is added at the end of each argument list.
norm.method = "cholesky" is the default and
reproduces the results of earlier versions exactly. The normalization is
the Cholesky factor of x'x. Because that factor is
constructed sequentially, the test statistics depend on the order in
which the columns of x are listed.
norm.method = "spectral" uses the symmetric square
root of the correlation matrix of the regressors, rescaled by their
standard deviations. The normalization is then free of any dependence on
the ordering of the columns of x, on the units in which
they are measured, and on their signs. Both choices give the same
limiting null distribution, therefore the same critical values apply and
both tests are valid.
Estimated break dates are unaffected by norm.method,
since they are obtained by minimizing the check function, which does not
depend on the normalization.
rq.break()