crqa (version 1.0.6)

optimizeParam: Optimal parameters value for CRQA on continuous time-series data

Description

Iterative procedure exploring a combination of parameter values to obtain maximal recurrence between two time-series. It finds the values for the three parameters of radius, delay and embedding dimensions that optimize recurrence.

Usage

optimizeParam(ts1, ts2, par, min.rec, max.rec)

Arguments

ts1

First time-series

ts2

Second time-series

par

A list of parameters for the optimization: lgM = a constant indicating maximum lag to inspect when calculating average mutual information between the two series. fnnpercent = the percentage of information gained, relative to the first embedding dimension, when higher embeddings are considered. radiusspan = the number of radi explored, relative to the standard deviation of the distance between the two series. typeami = decide on the minimum average mutual information. If typeami == mindip, then we select the lag at which minimal information is observed. If typeami == maxlag, then we select the maximum lag at which minimal information is observed.

min.rec

The minimum value of recurrence accepted. Default = 2

max.rec

The maximum value of recurrence accepted. Default = 5

Value

It returns a list with the following arguments:

radius

The optimal radius value found

emddim

Number of embedding dimensions

delay

The lag parameter.

Details

The optimization follows a three steps process:

1) Identify a delay that accommodates both time-series by finding the local minimum where mutual information between them drops, and starts to level off. When one ts has a considerably longer delay indicated than the another, the function selects the longer delay of the two to ensure that new information is gained for both. When the delays are close to each other, the function computes the mean of the two delays.

2) Determine embedding dimensions by using false nearest neighbors and checking when it bottoms out (i.e., there is no gain in adding more dimensions). If the embedding dimension for the two ts are different the algorithm selects the higher embedding dimension of the two to make sure that both time series are sufficiently unfolded.

3) Determine radius yielding a recurrence rate between 2-5 To do so, we first determine a starting radius that yields approximately 25 We generate a sampled sequence of equally spaced possible radi from such radius till 0, using as unit for the sequence step, the standard deviation of the distance matrix divided by a scaling parameter (radiusspan). The larger this parameter, the finer the unit. The size of the sample is specified by the user (radiussample).

References

Marwan, N., Carmen Romano, M., Thiel, M., and Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Physics Reports, 438(5), 237-329.

See Also

crqa, wincrqa

Examples

# NOT RUN {
## initialize the parameters

par = list(lgM =  20, steps = seq(1, 6, 1), 
radiusspan = 100, radiussample = 40, 
normalize = 0, rescale = 1, mindiagline = 2, 
minvertline = 2, tw = 0, whiteline = FALSE, 
recpt = FALSE, fnnpercent = 10, typeami = "mindip")


## generate two random uniform series

ts1 = runif(100)
ts2 = runif(100)

ans = optimizeParam(ts1, ts2, par, min.rec = 2, max.rec = 5)
print(ans)

## utilize leftmov, rightmov for an application to real-data
## reduce radiussample to increase computational speed

## data(crqa)
## ans = optimizeParam(leftmov, rightmov, par)
## print(ans)

# }