prodcomb {costat} R Documentation

## Combine two time series using a time-varying linear combination.

### Description

This function takes the `cfs` vector and splits it into two halves. The first half contains the wavelet coefficients for the `alpha` linear combination function, and the second half for the `beta` one. Then the functions themselves are generated by using the `coeftofn` function. Then, the coefficient functions are multiplied by the respective time series (`tsx` by `alpha` and `tsy` by `beta`) and the result returned.

### Usage

```prodcomb(cfs, tsx, tsy, filter.number = 1,
family = c("DaubExPhase", "DaubLeAsymm"), all = FALSE)
```

### Arguments

 `cfs` Wavelet coefficients of the two combination functions. The coefficients for alpha/beta combination functions are stored in the first/last half of the vector. `tsx` The x time series to combine `tsy` The y time series to combine `filter.number` The wavelet filter to use to obtain functions from coefficients `family` The wavelet family to do the same. `all` If TRUE then a list containing the combined series in the component `lcts` and the combination functions in components `alpha` and `beta`. Although the combined series is the thing that is usually later tested for stationarity, it is often useful to see, at some stage, what the combination functions are, as these provide interpretation as to what the combination might mean. If FALSE then just the combined series is returned.

### Details

This function is called by `findstysols` and makes use of `coeftofn` to turn coefficients into a function used in the combination.

### Value

If `all=TRUE` then a list with the following components:

 `lcts` The combined series, α_t X_t + β_t Y_t `alpha` The α_t combination function. `beta` The β_t combination function.

If `all=FALSE` then only `lcts` 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`, `coeftofn`

### Examples

```#
# Toy example
#
tmp.a <- c(1, -1)
tmp.b <- c(0.5, 0.5)
#
# Generate toy time series
#
xxx <- rnorm(256)
yyy <- rnorm(256)
#
# Combine xxx and yyy using the functions produced by inverse wavelet
# transform of tmp.a and tmp.b
#
## Not run: tmp <- prodcomb(c(tmp.a, tmp.b), tsx=xxx, tsy=yyy)
#
# E.g. plot combination
#
## Not run: ts.plot(tmp)
#
# Potentially test its stationarity.... etc
#
```

[Package costat version 2.4 Index]