# Plots solutions that are identified by findstysols

### Description

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.

### Usage

1 2 3 4 5 6 7 | ```
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", ...)
``` |

### Arguments

`res` |
Solution set returned by findstysols |

`tsx` |
The |

`tsy` |
The |

`inc` |
Adds an increment to the x-axis values. |

`solno` |
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) |

`filter.number` |
The wavelet filter number to use in reconstructing the linear combination function |

`family` |
The wavelet family to use in reconstructing the linear combination function. |

`plot.it` |
Currently unused in this function |

`spec.filter.number` |
This function computes the linear combination
time series and also then computes its EWS.
The wavelet ( |

`spec.family` |
The family of the wavelet used to compute the spectrum |

`plotcoef` |
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. |

`sameplot` |
If TRUE then the linear combination functions are plotted on the same plot. |

`norm` |
If TRUE then the linear combination functions are normalized
before plotting if |

`plotstystat` |
If TRUE (and if |

`plotsolinfo` |
If TRUE (and if |

`onlyacfs` |
Only plot the two acfs if |

`acfdatatrans` |
A function (e.g. |

`xlab` |
An x label for the time series plots, and spectral plots |

`...` |
Extra arguments for the acf plots. |

### Details

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.

### Value

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.

### Author(s)

Guy Nason

### References

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.

### See Also

`findstysols`

### Examples

1 2 3 | ```
#
# See examples in findstysols (the plot method for the results of
# findstysols make use of LCTSres)
``` |