LCTS {costat} R Documentation

## Computes a Linear Combination Test Statistics

### Description

Given a particular linear combination, specified in terms of coefficients, cfs, this functions forms the linear combination of two time series, tsx, tsy and returns the result of a stationarity test statistic on the combination.

### Usage

```LCTS(cfs, tsx, tsy, filter.number = 1,
family = c("DaubExPhase", "DaubLeAsymm"), plot.it = FALSE,
spec.filter.number = 1,
spec.family = c("DaubExPhase", "DaubLeAsymm"))
```

### Arguments

 `cfs` Coefficients describing the linear combination vectors. The first half correspond to the first vector (alpha) the second half to the beta vector. Hence this vector must have an even length, and each half has a length a power of two minus one. `tsx` The x time series `tsy` The y time series `filter.number` This function turns the coefficients into a linear combination function (e.g. alpha). This argument specifies the filter.number of the inverse wavelet transform that turns coefficients into a lc function. `family` Same as filter.number but for the wavelet family `plot.it` If TRUE then various things are plotted: both of the linear combination vectors/time series, the combined time series and its EWS estimate `spec.filter.number` The wavelet filter used to compute the EWS estimate `spec.family` The wavelet family used to compute the EWS estimate

### Details

This function forms a time-varying linear combination of two times series to form a third time series. Then a 'stationarity test' test statistic is applied to the third time series to compute how stationary (or non-stationary it is). This function is called by `findstysols` and actually does the work of forming the lc of two time series and gauging the stationarity

### Value

A single number which is the value of the test of stationarity for the combined time series. This is the result of `TOSts` but normalized for the squared coefficient norm

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`, `TOSts`, `coeftofn`

### Examples

```#
# Apply this function to random combination coefficients.
#
# The combination coefficients: comprised of two vectors each of length 3
# Note that 3 = 2^2 - 1, vectors need to be of length a power two minus 1
#
#	sret, fret are two time series in the package
#
data(sret)
data(fret)
LCTS( c(rnorm(3), rnorm(3)), sret, fret)
# 1.571728e-13
#
# The value of the test statistic is 1.57e-13
```

[Package costat version 2.4 Index]