% Time Series Analysis (Ver 3.20)% Schloegl A. (1996-2003) Time Series Analysis - A Toolbox for the use with Matlab. % WWW: http://www.dpmi.tu-graz.ac.at/~schloegl/matlab/tsa/%%	Version 3.20    Date: 10 May 2003%	Copyright (C) 1996-2003 by Alois Schloegl <a.schloegl@ieee.org>
%%  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)%   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 (planned in future)%   mvar	multivariate (vector) autoregressive estimation %   mvfilter	multivariate filter%   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鰃l, B. Kemp, T. Penzel, D. Kunz, S.-L. Himanen,A. V鋜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鰏ch G, Schl鰃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%% 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)