| Title: | Analysis of Nonlinear Time Series |
| Date: | 2013-04-29 |
| Version: | 0.1-13.1 |
| Author: | Antonio, Fabio Di Narzo |
| Depends: | R (≥ 2.2.0) |
| Imports: | deSolve |
| Suggests: | scatterplot3d |
| LazyData: | yes |
| LazyLoad: | yes |
| Description: | Routines for the analysis of nonlinear time series. This work is largely inspired by the TISEAN project, by Rainer Hegger, Holger Kantz and Thomas Schreiber: http://www.mpipks-dresden.mpg.de/~tisean/. |
| Maintainer: | Antonio Fabio Di Narzo <antonio.fabio@gmail.com> |
| License: | GPL-2 |
| Packaged: | 2019-01-07 12:11:22 UTC; hornik |
| Repository: | CRAN |
| Date/Publication: | 2019-01-07 12:21:28 UTC |
| NeedsCompilation: | yes |
Sample correlation integral
Description
Sample correlation integral for the specified length scale
Usage
C2(series, m, d, t, eps)
Arguments
series |
time series |
m |
embedding dimension |
d |
time delay |
t |
Theiler window |
eps |
length scale |
Details
Computes the sample correlation integral on the provided time series for the specified length scale, and considering a time window t (see references). It uses a naif algorithm: simply returns the fraction of points pairs nearer than eps. Normally, you would use d2, which takes roughly the same time, but computes the correlation sum for multiple length scales and embedding dimensions at once.
Value
The sample correlation integral at eps length scale.
Author(s)
Antonio, Fabio Di Narzo
References
Hegger, R., Kantz, H., Schreiber, T., Practical implementation of nonlinear time series methods: The TISEAN package; CHAOS 9, 413-435 (1999)
See Also
Tools to evaluate the maximal Lyapunov exponent of a dynamic system
Description
Tools to evaluate the maximal Lyapunov exponent of a dynamic system from a univariate time series
Usage
lyap_k(series, m, d, t, k=1, ref, s, eps)
lyap(dsts, start, end)
Arguments
series |
time series |
m |
embedding dimension |
d |
time delay |
k |
number of considered neighbours |
eps |
radius where to find nearest neighbours |
s |
iterations along which follow the neighbours of each point |
ref |
number of points to take into account |
t |
Theiler window |
dsts |
Should be the output of a call to |
start |
Starting time of the linear bite of |
end |
Ending time of the linear bite of |
Details
The function lyap_k estimates the largest Lyapunov exponent of a given scalar time series using the algorithm of Kantz.
The function lyap computes the regression coefficients of a user specified segment of the sequence given as input.
Value
lyap_k gives the logarithm of the stretching factor in time.
lyap gives the regression coefficients of the specified input sequence.
Author(s)
Antonio, Fabio Di Narzo
References
Hegger, R., Kantz, H., Schreiber, T., Practical implementation of nonlinear time series methods: The TISEAN package; CHAOS 9, 413-435 (1999)
M. T. Rosenstein, J. J. Collins, C. J. De Luca, A practical method for calculating largest Lyapunov exponents from small data sets, Physica D 65, 117 (1993)
See Also
mutual, false.nearest for the choice of optimal embedding parameters.
embedd to perform embedding.
Examples
output <-lyap_k(lorenz.ts, m=3, d=2, s=200, t=40, ref=1700, k=2, eps=4)
plot(output)
lyap(output, 0.73, 2.47)
Sample correlation integral (at multiple length scales)
Description
Computes the sample correlation integral over a grid of neps length scales starting from eps.min, and for multiple embedding dimensions
Usage
d2(series, m, d, t, eps.min, neps=100)
Arguments
series |
time series |
m |
max embedding dimension |
d |
time delay |
t |
Theiler window |
eps.min |
min length scale |
neps |
number of length scales to evaluate |
Details
Computes the sample correlation integral over neps length scales starting from eps.min, for embedding dimension 1,...,m , considering a t time window (see references). The slope of the linear segment in the log-log plot gives an estimate of the correlation dimension (see the example).
Value
Matrix. Column 1: length scales. Column i=2, ..., m+1: sample correlation integral for embedding dimension i-1.
Author(s)
Antonio, Fabio Di Narzo
References
Hegger, R., Kantz, H., Schreiber, T., Practical implementation of nonlinear time series methods: The TISEAN package; CHAOS 9, 413-435 (1999)
Examples
d2(lorenz.ts, m=6, d=2, t=4, eps.min=2)
Duffing oscillator
Description
Duffing oscillator system, to be used with sim.cont
Details
To be used with sim.cont
Author(s)
Antonio, Fabio Di Narzo
Embedding of a time series
Description
Embedding of a time series with provided time delay and embedding dimension parameters.
Usage
embedd(x, m, d, lags)
Arguments
x |
time series |
m |
embedding dimension (if lags missed) |
d |
time delay (if lags missed) |
lags |
vector of lags (if m and d are missed) |
Details
Embedding of a time series with provided delay and dimension parameters.
Value
Matrix with columns corresponding to lagged time series.
Author(s)
Antonio, Fabio Di Narzo. Multivariate time series patch by Jonathan Shore.
Examples
library(scatterplot3d)
x <- window(rossler.ts, start=90)
xyz <- embedd(x, m=3, d=8)
scatterplot3d(xyz, type="l")
## embedding multivariate time series
series <- cbind(seq(1,50),seq(101,150))
head(embedd(series, m=6, d=1))
Method of false nearest neighbours
Description
Method of false nearest neghbours to help deciding the optimal embedding dimension
Usage
false.nearest(series, m, d, t, rt=10, eps=sd(series)/10)
Arguments
series |
time series |
m |
maximum embedding dimension |
d |
delay parameter |
t |
Theiler window |
rt |
escape factor |
eps |
neighborhood diameter |
Details
Method of false nearest neighbours to help deciding the optimal embedding dimension.
Value
Fraction of false neighbors (first row) and total number of neighbors (second row) for each specified embedding dimension (columns)
Author(s)
Antonio, Fabio Di Narzo
References
Hegger, R., Kantz, H., Schreiber, T., Practical implementation of nonlinear time series methods: The TISEAN package; CHAOS 9, 413-435 (1999)
Kennel M. B., Brown R. and Abarbanel H. D. I., Determining embedding dimension for phase-space reconstruction using a geometrical construction, Phys. Rev. A, Volume 45, 3403 (1992).
Examples
(fn.out <- false.nearest(rossler.ts, m=6, d=8, t=180, eps=1, rt=3))
plot(fn.out)
Lorenz system
Description
Lorenz system, to be used with sim.cont
Details
To be used with sim.cont
Author(s)
Antonio, Fabio Di Narzo
Lorenz simulated time series, without noise
Description
Lorenz simulated time series, without noise. Of each state of the system, we observe the euclidean norm.
Details
Lorenz simulated time series, without noise, obtained with the call:
lorenz.ts <- sim.cont(lorenz.syst, 0, 100, 0.05, start.x=c(5,5,5), parms=c(10, 28, -8/3), obs.fun = function(x) sqrt(sum(x^2)))
Author(s)
Antonio, Fabio Di Narzo
Average Mutual Information
Description
Estimates the average mutual information index (ami) of a given time series for a specified number of lags
Usage
mutual(series, partitions = 16, lag.max = 20, plot=TRUE, ...)
Arguments
series |
time series |
partitions |
number of bins |
lag.max |
largest lag |
plot |
logical. If 'TRUE' (the default) the ami is plotted |
... |
further arguments to be passed to the plot method |
Details
Estimates the mutual information index for a specified number of lags. The joint probability distribution function is estimated with a simple bi-dimensional density histogram.
Value
An object of class "ami", which is a vector containing the estimated mutual information index for each lag between 0 and lag.max.
Author(s)
Antonio, Fabio Di Narzo
References
Hegger, R., Kantz, H., Schreiber, T., Practical implementation of nonlinear time series methods: The TISEAN package; CHAOS 9, 413-435 (1999)
Examples
mutual(lorenz.ts)
Plotting average mutual information index
Description
Plotting method for objects inheriting from class '"ami"'.
Usage
## S3 method for class 'ami'
plot(x, main = NULL, ...)
Arguments
x |
'"ami"' object |
main, ... |
additional graphical arguments |
Details
Plots the ami for each lag in x.
Author(s)
Antonio, Fabio Di Narzo
See Also
Plotting sample correlation integrals
Description
Plotting method for objects inheriting from class '"d2"'.
Usage
## S3 method for class 'd2'
plot(x, ...)
Arguments
x |
'"d2"' object |
... |
additional graphical arguments |
Details
Plots the sample correlation integrals in x in log-log scale, as a line for each considered embedding dimension.
Author(s)
Antonio, Fabio Di Narzo
See Also
Plotting false nearest neighbours results
Description
Plotting method for objects inheriting from class '"false.nearest"'.
Usage
## S3 method for class 'false.nearest'
plot(x, ...)
Arguments
x |
'"false.nearest"' object |
... |
additional graphical arguments |
Details
Plots the results of false.nearest.
Author(s)
Antonio, Fabio Di Narzo
See Also
Printing sample correlation integrals
Description
Printing method for objects inheriting from class '"d2"'.
Usage
## S3 method for class 'd2'
print(x, ...)
Arguments
x |
'"d2"' object |
... |
additional arguments to 'print' |
Details
Simply calls plot.d2.
Author(s)
Antonio, Fabio Di Narzo
See Also
Printing false nearest neighbours results
Description
Printing method for objects inheriting from class '"false.nearest"'.
Usage
## S3 method for class 'false.nearest'
print(x, ...)
Arguments
x |
'"false.nearest"' object |
... |
additional arguments to 'print' |
Details
Prints the table of results of false.nearest.
Author(s)
Antonio, Fabio Di Narzo
See Also
plot.false.nearest, false.nearest
Recurrence plot
Description
Recurrence plot
Usage
recurr(series, m, d, start.time=start(series), end.time=end(series), ...)
Arguments
series |
time series |
m |
embedding dimension |
d |
time delay |
start.time |
starting time window (in time units) |
end.time |
ending time window (in time units) |
... |
further parameters to be passed to |
Details
Produces the recurrence plot, as proposed by Eckmann et al. (1987). White is maximum distance, black is minimum.
warning
Be awared that number of distances to store goes as n^2, where n = length(window(series, start=start.time, end=end.time))!
Author(s)
Antonio, Fabio Di Narzo
References
Eckmann J.P., Oliffson Kamphorst S. and Ruelle D., Recurrence plots of dynamical systems, Europhys. Lett., volume 4, 973 (1987)
Examples
recurr(lorenz.ts, m=3, d=2, start.time=15, end.time=20)
Roessler system of equations
Description
Roessler system of equations
Details
To be used with sim.cont.
Author(s)
Antonio, Fabio Di Narzo
Roessler simulated time series, without noise
Description
Roessler simulated time series, without noise. Of each state of the system, we observe the first component.
Details
Roessler simulated time series, without noise, obtained with the call:
rossler.ts <- sim.cont(rossler.syst, start=0, end=650, dt=0.1, start.x=c(0,0,0), parms=c(0.15, 0.2, 10))
Author(s)
Antonio, Fabio Di Narzo
Simulates a continuous dynamic system
Description
Simulates a dynamic system of provided ODEs
Usage
sim.cont(syst, start.time, end.time, dt, start.x, parms=NULL, obs.fun=function(x) x[1])
Arguments
syst |
ODE system |
start.time |
starting time |
end.time |
ending time |
dt |
time between observations |
start.x |
initial conditions |
parms |
parameters for the system |
obs.fun |
observed function of the state |
Details
Simulates a dynamic system of provided ODEs.
Uses lsoda in odesolve for numerical integration of the system.
Value
The time series of the observed function of the system's state
Author(s)
Antonio, Fabio Di Narzo
See Also
lorenz.syst, rossler.syst, duffing.syst
Examples
rossler.ts <- sim.cont(rossler.syst, start=0, end=650, dt=0.1,
start.x=c(0,0,0), parms=c(0.15, 0.2, 10))
Space-time separation plot
Description
Space-time separation plot
Usage
stplot(series, m, d, idt=1, mdt)
Arguments
series |
time series |
m |
embedding dimension |
d |
time delay |
idt |
observation steps in each iteration |
mdt |
number of iterations |
Details
Produces the space-time separation plot, as introduced by Provenzale et al. (1992), which can be used to decide the Theiler time window t, which is required in many other algorithms in this package.
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 t between the points, as iso-lines at levels 10%, 20%, ..., 100%.
Value
lines of costant probability at 10%, 20%, ..., 100%.
Author(s)
Antonio, Fabio Di Narzo
References
Kantz H., Schreiber T., Nonlinear time series analysis. Cambridge University Press, (1997)
Provenzale A., Smith L. A., Vio R. and Murante G., Distiguishing between low-dimensional dynamics and randomness in measured time series. Physica D., volume 58, 31 (1992)
See Also
Examples
stplot(rossler.ts, m=3, d=8, idt=1, mdt=250)
Internal tseriesChaos objects
Description
Internal tseriesChaos objects.
Details
These are not to be called by the user.