LCTSres {costat} R Documentation

## 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

```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 `x` time series `tsy` The `y` time series `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.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. `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 `sameplot` is TRUE. This is so as to be able to compare the patterns in each function without regard to their overall size. `plotstystat` 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`. `plotsolinfo` If TRUE (and if `plotsolinfo=FALSE`) this option plots the α_t linear combination function, the β_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. `onlyacfs` Only plot the two acfs if `plotstystat=TRUE` `acfdatatrans` A function (e.g. `log`) to transform the series before taking and displaying the acf functions. `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.

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.

`findstysols`
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