Description Usage Arguments Details Author(s) References See Also Examples

A collection and description of functions to
investigate the chaotic behavior of time series
processes.

Functions to Analyse Chaotic Time Series:

`mutualPlot` | Returns mutual information, |

`falsennPlot` | returns false nearest neigbours, |

`recurrencePlot` | returns a recurrence plot, |

`separationPlot` | returns a space-time separation plot, |

`lyapunovPlot` | computes maximum lyapunov exponent. |

1 2 3 4 5 6 | ```
mutualPlot(x, partitions = 16, lag.max = 20, doplot = TRUE, ...)
falsennPlot(x, m, d, t, rt = 10, eps = NULL, doplot = TRUE, ...)
recurrencePlot(x, m, d, end.time, eps, nt = 10, doplot = TRUE, ...)
separationPlot(x, m, d, mdt, idt = 1, doplot = TRUE, ...)
lyapunovPlot(x, m, d, t, ref, s, eps, k = 1, doplot = TRUE, ...)
``` |

`d` |
an integer value setting the value of the time delay. |

`eps` |
[falsennPlot] - |

`doplot` |
a logical flag. Should a plot be displayed? |

`end.time` |
[recurrencePlot] - |

`idt` |
[separationPlot] - |

`k` |
[lyapunovPlot] - |

`lag.max` |
[mutualPlot] - |

`m` |
[*Plot] - |

`mdt` |
[separationPlot] - |

`nt` |
[recurrencePlot] - |

`rt` |
[falsennPlot] - |

`partitions` |
[mutualPlot] - |

`ref` |
[lyapunovPlot] - |

`s` |
[lyapunovPlot] - |

`t` |
[*Plot] - |

`x` |
[*Plot] - |

`...` |
arguments to be passed. |

**Phase Space Representation:**

The function `mutualPlot`

estimates and plots the mutual
information index of a given time series for a specified number
of lags. The joint probability distribution function is estimated
with a simple bi-dimensional density histogram.

The function `falsennPlot`

uses the Method of false nearest
neighbours to help deciding the optimal embedding dimension.

**Non-Stationarity:**

The funcdtion `recurrencePlot`

creates a recurrence plot as
proposed by Eckmann et al. [1987].

The function `separationPlot`

creates a space-time separation
plot qs introduced by Provenzale et al. [1992]. It plots the
probability that two points in the reconstructed phase-space have
distance smaller than epsilon in function of epsilon and of the
time between the points, as iso-lines at levels 10, 20, ..., 100
percent levels. The plot can be used to decide the Theiler time
window.

**Lyapunov Exponents:**

The function `lyapunovPlot`

evaluates and plots the largest
Lyapunov exponent of a dynamic system from a univariate time series.
The estimate of the Lyapunov exponent uses the algorithm of Kantz.
In addition, the function computes the regression coefficients of
a user specified segment of the sequence given as input.

**Dimensions and Entropies:**

The function `C2`

computes the sample correlation integral on
the provided time series for the specified length scale and
Theiler window. It uses a naiv algorithm: simply returns the
fraction of points pairs nearer than eps. It is prefarable to use
the function `d2`

, which takes roughly the same time, but
computes the correlation sum for multiple length scales and
embedding dimensions at once.

The function `d2`

computes the sample correlation integral
over given length scales `neps`

for embedding dimensions
`1:m`

for a given Theiler window. The slope of the linear
segment in the log-log plot gives an estimate of the correlation
dimension.

Diethelm Wuertz for the Rmetrics **R**-port.

Brock, W.A., Dechert W.D., Sheinkman J.A. (1987);
*A Test of Independence Based on the Correlation
Dimension*,
SSRI no. 8702, Department of Economics, University of
Wisconsin, Madison.

Eckmann J.P., Oliffson Kamphorst S., Ruelle D. (1987),
*Recurrence plots of dynamical systems*,
Europhys. Letters 4, 973.

Hegger R., Kantz H., Schreiber T. (1999);
*Practical implementation of nonlinear time series
methods: The TISEAN package*,
CHAOS 9, 413–435.

Kennel M.B., Brown R., Abarbanel H.D.I. (1992);
*Determining embedding dimension for phase-space
reconstruction using a geometrical construction*,
Phys. Rev. A45, 3403.

Rosenstein M.T., Collins J.J., De Luca C.J. (1993);
*A practical method for calculating largest Lyapunov
exponents from small data sets*,
Physica D 65, 117.

1 2 3 4 5 6 7 8 9 10 11 | ```
## mutualPlot -
mutualPlot(logisticSim(1000))
## recurrencePlot -
lorentz = lorentzSim(
times = seq(0, 40, by = 0.01),
parms = c(sigma = 16, r = 45.92, b = 4),
start = c(-14, -13, 47),
doplot = FALSE)
recurrencePlot(lorentz[, 2], m = 3, d = 2, end.time = 800, eps = 3,
nt = 5, pch = '.', cex = 2)
``` |

```
Loading required package: timeDate
Loading required package: timeSeries
Loading required package: fBasics
Rmetrics Package fBasics
Analysing Markets and calculating Basic Statistics
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org
Loading required package: fGarch
0 1 2 3 4 5 6 7
2.6101730 1.7394283 1.1875642 0.7399041 0.4859658 0.1802151 0.1385885 0.1355469
8 9 10 11 12 13 14 15
0.1331552 0.1456876 0.1317693 0.1201322 0.1232665 0.1081357 0.1117114 0.1217323
16 17 18 19 20
0.1197603 0.1241017 0.1258348 0.1132555 0.1206522
```

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