Plots lots of useful information concerning solutions identified using findstysols. It only plots those where the optimizer converged. Can additionally return the time-varying linear combination associated with any solution if plots are turned off.
LCTSres(res, tsx, tsy, inc = 0, solno = 1:nrow(res$endpar), filter.number = 1,
family = c("DaubExPhase", "DaubLeAsymm"), plot.it = FALSE,
spec.filter.number = 1,
spec.family = c("DaubExPhase", "DaubLeAsymm"), plotcoef = FALSE,
sameplot = TRUE, norm = FALSE, plotstystat = FALSE,
plotsolinfo = TRUE, onlyacfs = FALSE,
acfdatatrans = I, xlab = "Time", ...)The stationary solution, \(Z_t\), associated with the last solution
to be plotted is returned. Of course, if there is only one
solution to be plotted then it is the only possibility. Hence,
if all the plot arguments are FALSE then no plots are
produced and the stationary linear combination of the (last)
solution number is returned.
Solution set returned by findstysols
The x time series
The y time series
Adds an increment to the x-axis values.
Which solution number to look at. This can be a vector of solution numbers. The default is to look at all solutions (which can be a lot, depending on how many you've got)
The wavelet filter number to use in reconstructing the linear combination function
The wavelet family to use in reconstructing the linear combination function.
Currently unused in this function
This function computes the linear combination
time series and also then computes its EWS.
The wavelet (spec.filter.number is the filter number of
this wavelet) used to compute the EWS can be different to the
one used to compute the linear combination, as the latter is
only a means to an end - e.g. in principle, other basis functions
could be use in the linear combination. Also the spectrum
computed is only used to assess its constancy, so could be
a locally stationary Fourier one.
The family of the wavelet used to compute the spectrum
If TRUE then only the linear combination functions are plotted. If FALSE then a (set of potentially multiple) composite plot(s) are produced. These composite plots are what are usually most useful.
If TRUE then the linear combination functions are plotted on the same plot.
If TRUE then the linear combination functions are normalized
before plotting if sameplot is TRUE. This is so as to
be able to compare the patterns in each function without regard
to their overall size.
If TRUE (and if plotcoef=FALSE) this option
causes the function to plot statistics associated with the
stationary solution, \(Z_t\). The acf and partial acf are always
plotted. The time series plot of \(Z_t\) and its spectrum are
optionally plotted too if onlyacfs=FALSE.
If TRUE (and if plotsolinfo=FALSE) this
option plots the \(\alpha_t\) linear combination function,
the \(\beta_t\) one (ie both of them),
the stationary linear combination
\(Z_t\),
and an estimate of the EWS of \(Z_t\) computed using the
spec.filter.number and spec.family wavelet.
The variance associated with \(Z_t\) (the minimizing variance from
the optimizer in findstysols and the p-value
associated with the solution are displayed as plot titles.
Only plot the two acfs if plotstystat=TRUE
A function (e.g. log) to transform the series
before taking and displaying the acf functions.
An x label for the time series plots, and spectral plots
Extra arguments for the acf plots.
Guy Nason
The function findstysols takes two time series
and attempts to find time-varying linear combinations of the
two that are stationary. If one is found, we call it \(Z_t\).
However, findstysols works by numerical optimization,
typically from random starts, and, generally, there is no unique
stationary solution.
This function takes the results obtained by findstysols
in an object called res and then for a set of solutions
already identifed by the user, and supplied to this function
via solno, this function takes each identified solution
in turn and produces a set of plots.
Determining which solutions are interesting is another problem.
The COEFbothscale is a useful function which
can analyze all solution sets simultaneously and, usually, arrange
them into groups which are mutually similar. Then representative
members from each group can be further analyzed by
LCTSres.
Probably the most useful set of options is
plotcoef=FALSE and to issue a
par(mfrow=c(2,2)) command prior to running
LCTSres. This produces the plots, four to a page,
and enables interesting features to be compared from plot to plot.
The plotcoef=FALSE option causes four plots to be produced
(on the same page if mfrow is set as the previous paragraph
suggests). The first two are the (potentially) time-varying linear
combination functions, the next is the stationary linear
combination, \(Z_t\), itself and the final plot is an estimate of
the \(Z_t\)'s evolutionary wavelet spectrum. The titles of the latter
two plots display the process variance of \(Z_t\) (the global
unconditional variance, because \(Z_t\) is assumed to be stationary)
and the p-value associated the the hypothesis test of stationarity
of \(Z_t\). The spectral estimate show exhibit near constancy because
of the stationarity (as assessed by hypothesis test) of \(Z_t\).
If plotstystat=TRUE then further plots are produced
of the results of various classical time series analyses of \(Z_t\).
If onlyacfs=TRUE then only the acf and partial acf of \(Z_t\)
are plotted, otherwise \(Z_t\) and its classical spectrum are also
plotted (remember, \(Z_t\), has tested to be stationary and so these
classical methods are valid).
If more than one solution is to be plotted, then the scan()
function is employed to pause the plots between plots.
Cardinali, A. and Nason, Guy P. (2013) Costationarity of Locally Stationary Time Series Using costat. Journal of Statistical Software, 55, Issue 1.
Cardinali, A. and Nason, G.P. (2010) Costationarity of locally stationary time series. J. Time Series Econometrics, 2, Issue 2, Article 1.
findstysols
#
# See examples in findstysols (the plot method for the results of
# findstysols make use of LCTSres)
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