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PURPOSE ^

Time Series Analysis - A toolbox for the use with Matlab and Octave.

SYNOPSIS ^

This is a script file.

DESCRIPTION ^

 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)

CROSS-REFERENCE INFORMATION ^

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