costat (version 1.1-1)

COEFbothscale: Produces plots from output of findstysol that attempt to group different solutions.

Description

Uses hierarchical clustering and multidimensional scaling to produce a plot of all the convergence stationary solutions. These plots are designed to aid the user in identifying `unique' sets of stationary solutions.

Usage

COEFbothscale(l, plotclustonly = FALSE, ...)

Arguments

l

An object returned by findstysols, which contains the results of an optimization to find solutions that correspond to stationary series which are the time-varying linear combination of two locally s

plotclustonly

If TRUE then only produce the hierarchical clustering plot.

...

Additional arguments to the hierarchical clustering plot.

Value

• The results of the multidimensional scaling and hierarchical clustering are returned as list with two components epscale and epclust respectively.

Details

The function findstysols runs multiple optimization runs (it can do only one is required) to try and find (multiple) solutions to the problem of finding costationary time series. It does this by running the optimization from multiple random starts. The solutions (if they exist) to these optimizations are not necessarily unique, and it is useful to find as many genuine different solutions as possible. However, even if there was one unique (mathematical) solution, due to different random starts, the vagaries of the optimizer, and the fact that the hypothesis test for stationarity is not a deterministic test, it is usually the case the many solutions very close to, but not identical to, the unique solutions might be found. However, they would morally be thought to be the same solution.

In the case of multiple actual solutions, then the optimization algorithm might find many solutions close to the real ones and, of course, it might completely miss a real one (or not be near to a real one). However, the situation often arises where, after multiple starts, one ends up with clusters of computed solutions that group themselves around the `real' solution.

In other words, the solution vectors can be viewed as a multivariate data set where the cases correspond to the results of different optimization runs and the variables correspond to the coefficients of the time-varying linear combinations.

Both multidimensional scaling (cmdscale) and hiearchical clustering (hclust) are used to determine possible clusterings of solutions. Then, representative members from these clusters can be further investigated with a function such as LCTSres

References

`Costationary and stationarity tests for stock index returns' by Cardinali and Nason

See Also

COEFscale,findstysols, LCTSres

Examples

#
# To be run directly after the example in findstysols
#
COEFbothscale(tmp)