Time Series Analysis - A toolbox for the use with Matlab and Octave.
$Id: contents.m 5090 2008-06-05 08:12:04Z schloegl $
Copyright (C) 1996-2004,2008 by Alois Schloegl <a.schloegl@ieee.org>
WWW: http://hci.tugraz.at/~schloegl/matlab/tsa/
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Time Series Analysis - a toolbox for the use with Matlab
aar adaptive autoregressive estimator
acovf (*) Autocovariance function
acorf (acf) (*) autocorrelation function
pacf (*) partial autocorrelation function, includes signifcance test and confidence interval
parcor (*) partial autocorrelation function
biacovf biautocovariance function (3rd order cumulant)
bispec Bi-spectrum
durlev (*) solves Yule-Walker equation - converts ACOVF into AR parameters
lattice (*) calcultes AR parameters with lattice method
lpc (*) calculates the prediction coefficients form a given time series
invest0 (*) a prior investigation (used by invest1)
invest1 (*) investigates signal (useful for 1st evaluation of the data)
rmle AR estimation using recursive maximum likelihood function
selmo (*) Select Order of Autoregressive model using different criteria
histo (*) histogram
hup (*) test Hurwitz polynomials
ucp (*) test Unit Circle Polynomials
y2res (*) computes mean, variance, skewness, kurtosis, entropy, etc. from data series
ar_spa (*) spectral analysis based on the autoregressive model
detrend (*) removes trend, can handle missing values, non-equidistant sampled data
flix floating index, interpolates data for non-interger indices
Multivariate analysis
adim adaptive information matrix (inverse correlation matrix)
mvar multivariate (vector) autoregressive estimation
mvaar multivariate adaptvie autoregressive estimation using Kalman filtering
mvfilter multivariate filter
mvfreqz multivariate spectra
arfit2 provides compatibility to ARFIT [Schneider and Neumaier, 2001]
Conversions between Autocorrelation (AC), Autoregressive parameters (AR),
prediction polynom (POLY) and Reflection coefficient (RC)
ac2poly (*) transforms autocorrelation into prediction polynom
ac2rc (*) transforms autocorrelation into reflexion coefficients
ar2rc (*) transforms autoregressive parameters into reflection coefficients
rc2ar (*) transforms reflection coefficients into autoregressive parameters
poly2ac (*) transforms polynom to autocorrelation
poly2ar (*) transforms polynom to AR
poly2rc (*)
rc2ac (*)
rc2poly (*)
ar2poly (*)
Utility functions
sinvest1 shows the parameter calculated by INVEST1
Test suites
tsademo demonstrates INVEST1 on EEG data
invfdemo demonstration of matched, inverse filtering
bisdemo demonstrates bispectral estimation
(*) indicates univariate analysis of multiple data series (each in a row) can be processed.
(-) indicates that these functions will be removed in future
REFERENCES (sources):
http://www.itl.nist.gov/
http://mathworld.wolfram.com/
P.J. Brockwell and R.A. Davis 'Time Series: Theory and Methods', 2nd ed. Springer, 1991.
O. Foellinger 'Lineare Abtastsysteme', Oldenburg Verlag, Muenchen, 1986.
F. Gausch 'Systemtechnik', Textbook, University of Technology Graz, 1993.
M.S. Grewal and A.P. Andrews 'Kalman Filtering' Prentice Hall, 1993.
S. Haykin 'Adaptive Filter Theory' 3ed. Prentice Hall, 1996.
E.I. Jury 'Theory and Application of the z-Transform Method', Robert E. Krieger Publishing Co., 1973.
M.S. Kay 'Modern Spectal Estimation' Prentice Hall, 1988.
Ch. Langraf and G. Schneider 'Elemente der Regeltechnik', Springer Verlag, 1970.
S.L. Marple 'Digital Spetral Analysis with Applications' Prentice Hall, 1987.
C.L. Nikias and A.P. Petropulu 'Higher-Order Spectra Analysis' Prentice Hall, 1993.
M.B. Priestley 'Spectral Analysis and Time Series' Academic Press, 1981.
T. Schneider and A. Neumaier 'Algorithm 808: ARFIT - a matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models'
ACM Transactions on Mathematical software, 27(Mar), 58-65.
C.E. Shannon and W. Weaver 'The mathematical theory of communication' University of Illinois Press, Urbana 1949 (reprint 1963).
W.S. Wei 'Time Series Analysis' Addison Wesley, 1990.
REFERENCES (applications):
[1] A. Schl�l, B. Kemp, T. Penzel, D. Kunz, S.-L. Himanen,A. V�ri, G. Dorffner, G. Pfurtscheller.
Quality Control of polysomnographic Sleep Data by Histogram and Entropy Analysis.
Clin. Neurophysiol. 1999, Dec; 110(12): 2165 - 2170.
[2] Penzel T, Kemp B, Kl�ch G, Schl�l A, Hasan J, Varri A, Korhonen I.
Acquisition of biomedical signals databases
IEEE Engineering in Medicine and Biology Magazine 2001, 20(3): 25-32
[3] Alois Schl�l (2000)
The electroencephalogram and the adaptive autoregressive model: theory and applications
Shaker Verlag, Aachen, Germany,(ISBN3-8265-7640-3).
Features:
- Multiple Signal Processing
- Efficient algorithms
- Model order selection tools
- higher (3rd) order analysis
- Maximum entropy spectral estimation
- can deal with missing values (NaN's)