## Delta test

Purpose

Description

Macro Synopsis

Modules

Related Functions

References

### Purpose

Delta test for detecting dependencies between two time series.

### Description

The Delta test is designed to detect dependencies between a group of
signals and a reference signal. Furthermore it is suited to
give an upper limit for the noise in the reference signal.
On the one hand the test is based on the common
-definition of continuity, on the other hand
on the correlation integral.

An arbitrary number of signals are taken as input signals. The first input
signal is considered the reference signal. "Delta test" calculates an
dependability index for each of the other signals with respect to the
reference signal. These indices are returned in the output signal y. The
total dependability and the upper Gauss noise limit of the reference signal
are displayed in the message window, together with the dependability indices.

The only parameter is

- the algorithm used for "Delta test":
- "Standard" (0),
- "Greedy" (1) or
- "Threshold Accepting" (2)

"Greedy" and "Threshold Accepting" are optimisation algorithms for finding the
set of independent variables representing the reference time series with a
certain trade-off between computation speed and accuracy.
The Greedy-algorithm works by successively building up the vector of
independent variables until it is complete and thus the embedding dimension
is reached. The Threshold Accepting algorithm performs a local / neighbourhood
search based on Simulated Annealing.

Note that since this function operates on a 'pure' time series, the scale and the shift of the given signal do not affect the result.

### Macro Synopsis

`y = DeltaTest(x,algo);`

signal x[];

signal y;

option algo;

### Modules

Nonlinear

### Related Functions

BDS test,
Conditional coupling divergence (PCCD), Mutual cross information,
Pointwise transinformation, Post event scan,
Synchronicity histogram, Transinformation.

### References

Pi/Peterson [25]