tos object.After a test of stationarity for dyadic data
(e.g. hwtos2)
is applied to a time series it generates a results object of
class tos. This function takes objects of that
class and produces a graphical representation of the test.
# S3 method for tos
plot(x, mctype = "FDR", sub = NULL, xlab = "Time",
arrow.length = 0.05, verbose = FALSE, ...)None.
The tos class object, the results of the
test of stationarity that you wish to plot.
Whether you wish to see rejections (if they exist)
according to a Bonferroni assessment ("BON") or
according to FDR ("FDR")
An argument to change the subtitle.
An argument to change the x-axis label.
The length of the edges of the arrow
head (in inches). Note that this is the argument that is
supplied as the length argument of the arrow
function that is called by this routine to draw the arrows.
If TRUE then some meaningless debugging
information is printed.
Other arguments to the main ts.plot routine that
does the plotting.
Guy Nason.
The following things are usually plotted. 1. The time series that was investigated. The left-hand axes is that for the time series. The horizontal axis is time (but just integers indexing). If the series was deemed stationary by the test then that's it except that the subtitle indicates that no Haar wavelet coefficients were rejected as being nonzero.
If the test indicated that the series was nonstationary then
the subtitle indicates this by stating the number of rejections
(this might be according to FDR or Bonferroni depending on
the setting of the mctype argument. Then graphical
representations of any significant Haar wavelet coefficients
are plotted as double-headed red horizontal arrows on the plot.
The horizontal extent corresponds to the support of the underlying
wavelet. The vertical position of the arrows gives an indication
of the wavelet periodogram scale where the significant coefficient
was found. The wavelet periodogram scales are indexed by the right
hand axis, and beware, the numbers might not be consecutive, but
they will be ordered (so e.g. if no signficant coefficients were
discovered at wavelet periodogram scale level 6, then that scale/axis
label will not appear). The scale within the Haar wavelet transform
is indicated by the vertical position WITHIN ticks between
wavelet periodogram scales (ie, there are TWO scales: the wavelet
periodogram scale that is currently being analyzed, and the
Haar wavelet transform scale within the periodogram scale).
So, if two right hand axis labels are, e.g., 4 and 5, and
horizontal arrows appear between these two they actually correspond
to different Haar wavelet transform scales AT wavelet periodogram
level 4. It is not usually possible to tell precisely which
Haar wavelet transform scale the coefficients can come from,
but the information can be extracted from the summary.tos
function which lists this.
Nason, G.P. (2013) A test for second-order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series. J. R. Statist. Soc. B, 75, 879-904. tools:::Rd_expr_doi("10.1111/rssb.12015")
hwtos2, summary.tos
#
# Produces an interesting plot with high probability
#
#
# Note that the input time series is two concatenated white noise
# sequences with very different variances.
#
answer <- hwtos2(c(rnorm(256), rnorm(256, sd=5)))
if (FALSE) plot(answer)
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