--- /dev/null
+# Created by Octave 3.6.1, Thu Apr 05 12:32:56 2012 UTC <root@brouzouf>
+# name: cache
+# type: cell
+# rows: 3
+# columns: 55
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+aar
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2198
+ Calculates adaptive autoregressive (AAR) and adaptive autoregressive moving average estimates (AARMA)
+ of real-valued data series using Kalman filter algorithm.
+ [a,e,REV] = aar(y, mode, MOP, UC, a0, A, W, V);
+
+ The AAR process is described as following
+ y(k) - a(k,1)*y(t-1) -...- a(k,p)*y(t-p) = e(k);
+ The AARMA process is described as following
+ y(k) - a(k,1)*y(t-1) -...- a(k,p)*y(t-p) = e(k) + b(k,1)*e(t-1) + ... + b(k,q)*e(t-q);
+
+ Input:
+ y Signal (AR-Process)
+ Mode is a two-element vector [aMode, vMode],
+ aMode determines 1 (out of 12) methods for updating the co-variance matrix (see also [1])
+ vMode determines 1 (out of 7) methods for estimating the innovation variance (see also [1])
+ aMode=1, vmode=2 is the RLS algorithm as used in [2]
+ aMode=-1, LMS algorithm (signal normalized)
+ aMode=-2, LMS algorithm with adaptive normalization
+
+ MOP model order, default [10,0]
+ MOP=[p] AAR(p) model. p AR parameters
+ MOP=[p,q] AARMA(p,q) model, p AR parameters and q MA coefficients
+ UC Update Coefficient, default 0
+ a0 Initial AAR parameters [a(0,1), a(0,2), ..., a(0,p),b(0,1),b(0,2), ..., b(0,q)]
+ (row vector with p+q elements, default zeros(1,p) )
+ A Initial Covariance matrix (positive definite pxp-matrix, default eye(p))
+ W system noise (required for aMode==0)
+ V observation noise (required for vMode==0)
+
+ Output:
+ a AAR(MA) estimates [a(k,1), a(k,2), ..., a(k,p),b(k,1),b(k,2), ..., b(k,q]
+ e error process (Adaptively filtered process)
+ REV relative error variance MSE/MSY
+
+
+ Hint:
+ The mean square (prediction) error of different variants is useful for determining the free parameters (Mode, MOP, UC)
+
+ REFERENCE(S):
+ [1] A. Schloegl (2000), The electroencephalogram and the adaptive autoregressive model: theory and applications.
+ ISBN 3-8265-7640-3 Shaker Verlag, Aachen, Germany.
+
+ More references can be found at
+ http://www.dpmi.tu-graz.ac.at/~schloegl/publications/
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ Calculates adaptive autoregressive (AAR) and adaptive autoregressive moving ave
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+aarmam
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1372
+ Estimating Adaptive AutoRegressive-Moving-Average-and-mean model (includes mean term)
+
+ !! This function is obsolete and is replaced by AMARMA
+
+ [z,E,REV,ESU,V,Z,SPUR] = aarmam(y, mode, MOP, UC, z0, Z0, V0, W);
+ Estimates AAR parameters with Kalman filter algorithm
+ y(t) = sum_i(a_i(t)*y(t-i)) + m(t) + e(t) + sum_i(b_i(t)*e(t-i))
+
+ State space model
+ z(t) = G*z(t-1) + w(t) w(t)=N(0,W)
+ y(t) = H*z(t) + v(t) v(t)=N(0,V)
+
+ G = I,
+ z = [m(t),a_1(t-1),..,a_p(t-p),b_1(t-1),...,b_q(t-q)];
+ H = [1,y(t-1),..,y(t-p),e(t-1),...,e(t-q)];
+ W = E{(z(t)-G*z(t-1))*(z(t)-G*z(t-1))'}
+ V = E{(y(t)-H*z(t-1))*(y(t)-H*z(t-1))'}
+
+
+ Input:
+ y Signal (AR-Process)
+ Mode determines the type of algorithm
+
+ MOP Model order [m,p,q], default [0,10,0]
+ m=1 includes the mean term, m=0 does not.
+ p and q must be positive integers
+ it is recommended to set q=0.
+ UC Update Coefficient, default 0
+ z0 Initial state vector
+ Z0 Initial Covariance matrix
+
+ Output:
+ z AR-Parameter
+ E error process (Adaptively filtered process)
+ REV relative error variance MSE/MSY
+
+ REFERENCE(S):
+ [1] A. Schloegl (2000), The electroencephalogram and the adaptive autoregressive model: theory and applications.
+ ISBN 3-8265-7640-3 Shaker Verlag, Aachen, Germany.
+
+ More references can be found at
+ http://pub.ist.ac.at/~schloegl/publications/
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ Estimating Adaptive AutoRegressive-Moving-Average-and-mean model (includes mean
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+ac2poly
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 179
+ converts the autocorrelation sequence into an AR polynomial
+ [A,Efinal] = ac2poly(r)
+
+ see also ACOVF ACORF AR2RC RC2AR DURLEV AC2POLY, POLY2RC, RC2POLY, RC2AC, AC2RC, POLY2AC
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ converts the autocorrelation sequence into an AR polynomial
+ [A,Efinal] = ac2po
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+ac2rc
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 182
+ converts the autocorrelation function into reflection coefficients
+ [RC,r0] = ac2rc(r)
+
+ see also ACOVF ACORF AR2RC RC2AR DURLEV AC2POLY, POLY2RC, RC2POLY, RC2AC, AC2RC, POLY2AC
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ converts the autocorrelation function into reflection coefficients
+ [RC,r0] =
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+acorf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1078
+ Calculates autocorrelations for multiple data series.
+ Missing values in Z (NaN) are considered.
+ Also calculates Ljung-Box Q stats and p-values.
+
+ [AutoCorr,stderr,lpq,qpval] = acorf(Z,N);
+ If mean should be removed use
+ [AutoCorr,stderr,lpq,qpval] = acorf(detrend(Z',0)',N);
+ If trend should be removed use
+ [AutoCorr,stderr,lpq,qpval] = acorf(detrend(Z')',N);
+
+ INPUT
+ Z is data series for which autocorrelations are required
+ each in a row
+ N maximum lag
+
+ OUTPUT
+ AutoCorr nr x N matrix of autocorrelations
+ stderr nr x N matrix of (approx) std errors
+ lpq nr x M matrix of Ljung-Box Q stats
+ qpval nr x N matrix of p-values on Q stats
+
+ All input and output parameters are organized in rows, one row
+ corresponds to one series
+
+ REFERENCES:
+ S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
+ M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+ W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+ J.S. Bendat and A.G.Persol "Random Data: Analysis and Measurement procedures", Wiley, 1986.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 55
+ Calculates autocorrelations for multiple data series.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+acovf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 826
+ ACOVF estimates autocovariance function (not normalized)
+ NaN's are interpreted as missing values.
+
+ [ACF,NN] = acovf(Z,MAXLAG,Mode);
+
+ Input:
+ Z Signal (one channel per row);
+ MAXLAG maximum lag
+ Mode 'biased' : normalizes with N [default]
+ 'unbiased': normalizes with N-lag
+ 'coeff' : normalizes such that lag 0 is 1
+ others : no normalization
+
+ Output:
+ ACF autocovariance function
+ NN number of valid elements
+
+ REFERENCES:
+ A.V. Oppenheim and R.W. Schafer, Digital Signal Processing, Prentice-Hall, 1975.
+ S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
+ M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+ W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+ J.S. Bendat and A.G.Persol "Random Data: Analysis and Measurement procedures", Wiley, 1986.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ ACOVF estimates autocovariance function (not normalized)
+ NaN's are interpreted
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+adim
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 659
+ ADIM adaptive information matrix. Estimates the inverse
+ correlation matrix in an adaptive way.
+
+ [IR, CC] = adim(U, UC [, IR0 [, CC0]]);
+ U input data
+ UC update coefficient 0 < UC << 1
+ IR0 initial information matrix
+ CC0 initial correlation matrix
+ IR information matrix (inverse correlation matrix)
+ CC correlation matrix
+
+ The algorithm uses the Matrix Inversion Lemma, also known as
+ "Woodbury's identity", to obtain a recursive algorithm.
+ IR*CC - UC*I should be approx. zero.
+
+ Reference(s):
+ [1] S. Haykin. Adaptive Filter Theory, Prentice Hall, Upper Saddle River, NJ, USA
+ pp. 565-567, Equ. (13.16), 1996.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 34
+ ADIM adaptive information matrix.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+amarma
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1501
+ Adaptive Mean-AutoRegressive-Moving-Average model estimation
+ [z,E,ESU,REV,V,Z,SPUR] = amarma(y, mode, MOP, UC, z0, Z0, V0, W);
+ Estimates AAR parameters with Kalman filter algorithm
+ y(t) = sum_i(a(i,t)*y(t-i)) + mu(t) + E(t)
+
+ State space model:
+ z(t)=G*z(t-1) + w(t) w(t)=N(0,W)
+ y(t)=H*z(t) + v(t) v(t)=N(0,V)
+
+ G = I,
+ z = [µ(t)/(1-sum_i(a(i,t))),a_1(t-1),..,a_p(t-p),b_1(t-1),...,b_q(t-q)];
+ H = [1,y(t-1),..,y(t-p),e(t-1),...,e(t-q)];
+ W = E{(z(t)-G*z(t-1))*(z(t)-G*z(t-1))'}
+ V = E{(y(t)-H*z(t-1))*(y(t)-H*z(t-1))'}
+
+ Input:
+ y Signal (AR-Process)
+ Mode
+ [0,0] uses V0 and W
+
+ MOP Model order [m,p,q], default [0,10,0]
+ m=1 includes the mean term, m=0 does not.
+ p and q must be positive integers
+ it is recommended to set q=0.
+ UC Update Coefficient, default 0
+ z0 Initial state vector
+ Z0 Initial Covariance matrix
+
+ Output:
+ z AR-Parameter
+ E error process (Adaptively filtered process)
+ REV relative error variance MSE/MSY
+
+
+ see also: AAR
+
+ REFERENCE(S):
+ [1] A. Schloegl (2000), The electroencephalogram and the adaptive autoregressive model: theory and applications.
+ ISBN 3-8265-7640-3 Shaker Verlag, Aachen, Germany.
+ [2] Schlögl A, Lee FY, Bischof H, Pfurtscheller G
+ Characterization of Four-Class Motor Imagery EEG Data for the BCI-Competition 2005.
+ Journal of neural engineering 2 (2005) 4, S. L14-L22
+
+ More references can be found at
+ http://www.dpmi.tu-graz.ac.at/~schloegl/publications/
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ Adaptive Mean-AutoRegressive-Moving-Average model estimation
+ [z,E,ESU,REV,V,Z,
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+ar2poly
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 603
+ converts autoregressive parameters into AR polymials
+ Multiple polynomials can be converted.
+ function [A] = ar2poly(AR);
+
+ INPUT:
+ AR AR parameters, each row represents one set of AR parameters
+
+ OUTPUT
+ A denominator polynom
+
+
+ see also ACOVF ACORF DURLEV RC2AR FILTER FREQZ ZPLANE
+
+ REFERENCES:
+ P.J. Brockwell and R. A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+ S. Haykin "Adaptive Filter Theory" 3rd ed. Prentice Hall, 1996.
+ M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+ W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ converts autoregressive parameters into AR polymials
+ Multiple polynomials can
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+ar2rc
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1007
+ converts autoregressive parameters into reflection coefficients
+ with the Durbin-Levinson recursion for multiple channels
+ function [AR,RC,PE] = ar2rc(AR);
+ function [MX,PE] = ar2rc(AR);
+
+ INPUT:
+ AR autoregressive model parameter
+
+ OUTPUT
+ AR autoregressive model parameter
+ RC reflection coefficients (= -PARCOR coefficients)
+ PE remaining error variance (relative to PE(1)=1)
+ MX transformation matrix between ARP and RC (Attention: needs O(p^2) memory)
+ AR = MX(:,K*(K-1)/2+(1:K));
+ RC = MX(:,(1:K).*(2:K+1)/2);
+
+ All input and output parameters are organized in rows, one row
+ corresponds to the parameters of one channel
+
+ see also ACOVF ACORF DURLEV RC2AR
+
+ REFERENCES:
+ P.J. Brockwell and R. A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+ S. Haykin "Adaptive Filter Theory" 3rd ed. Prentice Hall, 1996.
+ M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+ W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ converts autoregressive parameters into reflection coefficients
+ with the Durb
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+ar_spa
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1259
+ AR_SPA decomposes an AR-spectrum into its compontents
+ [w,A,B,R,P,F,ip] = ar_spa(AR,fs,E);
+
+ INPUT:
+ AR autoregressive parameters
+ fs sampling rate, provide w and B in [Hz], if not given the result is in radians
+ E noise level (mean square), gives A and F in units of E, if not given as relative amplitude
+
+ OUTPUT
+ w center frequency
+ A Amplitude
+ B bandwidth
+ - less important output parameters -
+ R residual
+ P poles
+ ip number of complex conjugate poles
+ real(F) power, absolute values are obtained by multiplying with noise variance E(p+1)
+ imag(F) assymetry, - " -
+
+ All input and output parameters are organized in rows, one row
+ corresponds to the parameters of one channel
+
+ see also ACOVF ACORF DURLEV IDURLEV PARCOR YUWA
+
+ REFERENCES:
+ [1] Zetterberg L.H. (1969) Estimation of parameter for linear difference equation with application to EEG analysis. Math. Biosci., 5, 227-275.
+ [2] Isaksson A. and Wennberg, A. (1975) Visual evaluation and computer analysis of the EEG - A comparison. Electroenceph. clin. Neurophysiol., 38: 79-86.
+ [3] G. Florian and G. Pfurtscheller (1994) Autoregressive model based spectral analysis with application to EEG. IIG - Report Series, University of Technolgy Graz, Austria.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ AR_SPA decomposes an AR-spectrum into its compontents
+ [w,A,B,R,P,F,ip] = ar_s
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+arcext
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 738
+ ARCEXT extracts AR and RC of order P from Matrix MX
+ function [AR,RC] = arcext(MX,P);
+
+ INPUT:
+ MX AR and RC matrix calculated by durlev
+ P model order (default maximum possible)
+
+ OUTPUT
+ AR autoregressive model parameter
+ RC reflection coefficients (= -PARCOR coefficients)
+
+ All input and output parameters are organized in rows, one row
+ corresponds to the parameters of one channel
+
+ see also ACOVF ACORF DURLEV
+
+ REFERENCES:
+ P.J. Brockwell and R. A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+ S. Haykin "Adaptive Filter Theory" 3rd ed. Prentice Hall, 1996.
+ M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+ W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ ARCEXT extracts AR and RC of order P from Matrix MX
+ function [AR,RC] = arcext
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+arfit2
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1227
+ ARFIT2 estimates multivariate autoregressive parameters
+ of the MVAR process Y
+
+ Y(t,:)' = w' + A1*Y(t-1,:)' + ... + Ap*Y(t-p,:)' + x(t,:)'
+
+ ARFIT2 uses the Nutall-Strand method (multivariate Burg algorithm)
+ which provides better estimates the ARFIT [1], and uses the
+ same arguments. Moreover, ARFIT2 is faster and can deal with
+ missing values encoded as NaNs.
+
+ [w, A, C, sbc, fpe] = arfit2(v, pmin, pmax, selector, no_const)
+
+ INPUT:
+ v data - each channel in a column
+ pmin, pmax minimum and maximum model order
+ selector 'fpe' or 'sbc' [default]
+ no_const 'zero' indicates no bias/offset need to be estimated
+ in this case is w = [0, 0, ..., 0]';
+
+ OUTPUT:
+ w mean of innovation noise
+ A [A1,A2,...,Ap] MVAR estimates
+ C covariance matrix of innovation noise
+ sbc, fpe criteria for model order selection
+
+ see also: ARFIT, MVAR
+
+ REFERENCES:
+ [1] A. Schloegl, 2006, Comparison of Multivariate Autoregressive Estimators.
+ Signal processing, p. 2426-9.
+ [2] T. Schneider and A. Neumaier, 2001.
+ 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.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ ARFIT2 estimates multivariate autoregressive parameters
+ of the MVAR process Y
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+biacovf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 228
+ BiAutoCovariance function
+ [BiACF] = biacovf(Z,N);
+
+ Input: Z Signal
+ N # of coefficients
+ Output: BIACF bi-autocorrelation function (joint cumulant 3rd order
+ Output: ACF covariance function (joint cumulant 2nd order)
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 53
+ BiAutoCovariance function
+ [BiACF] = biacovf(Z,N);
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+bisdemo
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 48
+ BISDEMO (script) Shows BISPECTRUM of eeg8s.mat
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 44
+ BISDEMO (script) Shows BISPECTRUM of eeg8s.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+bispec
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 382
+ Calculates Bispectrum
+ [BISPEC] = bispec(Z,N);
+
+ Input: Z Signal
+ N # of coefficients
+ Output: BiACF bi-autocorrelation function = 3rd order cumulant
+ BISPEC Bi-spectrum
+
+ Reference(s):
+ C.L. Nikias and A.P. Petropulu "Higher-Order Spectra Analysis" Prentice Hall, 1993.
+ M.B. Priestley, "Non-linear and Non-stationary Time series Analysis", Academic Press, London, 1988.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 49
+ Calculates Bispectrum
+ [BISPEC] = bispec(Z,N);
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+content
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1809
+ Time Series Analysis (Ver 3.10)
+ Schloegl A. (1996-2003,2008) Time Series Analysis - A Toolbox for the use with Matlab.
+ WWW: http://hci.tugraz.at/~schloegl/matlab/tsa/
+
+ $Id: content.m 5090 2008-06-05 08:12:04Z schloegl $
+ Copyright (C) 1996-2003,2008 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
+ quantiles calculates quantiles
+
+ Multivariate analysis (planned in future)
+ mvar multivariate (vector) autoregressive estimation
+ mvfilter multivariate filter
+ arfit2 provides compatibility to ARFIT [Schneider and Neumaier, 2001]
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 29
+ Time Series Analysis (Ver 3.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+contents
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5874
+ 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. Schlögl, B. Kemp, T. Penzel, D. Kunz, S.-L. Himanen,A. Värri, 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, Klösch G, Schlögl 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 Schlögl (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)
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 69
+ Time Series Analysis - A toolbox for the use with Matlab and Octave.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+covm
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1182
+ COVM generates covariance matrix
+ X and Y can contain missing values encoded with NaN.
+ NaN's are skipped, NaN do not result in a NaN output.
+ The output gives NaN only if there are insufficient input data
+
+ COVM(X,Mode);
+ calculates the (auto-)correlation matrix of X
+ COVM(X,Y,Mode);
+ calculates the crosscorrelation between X and Y
+ COVM(...,W);
+ weighted crosscorrelation
+
+ Mode = 'M' minimum or standard mode [default]
+ C = X'*X; or X'*Y correlation matrix
+
+ Mode = 'E' extended mode
+ C = [1 X]'*[1 X]; % l is a matching column of 1's
+ C is additive, i.e. it can be applied to subsequent blocks and summed up afterwards
+ the mean (or sum) is stored on the 1st row and column of C
+
+ Mode = 'D' or 'D0' detrended mode
+ the mean of X (and Y) is removed. If combined with extended mode (Mode='DE'),
+ the mean (or sum) is stored in the 1st row and column of C.
+ The default scaling is factor (N-1).
+ Mode = 'D1' is the same as 'D' but uses N for scaling.
+
+ C = covm(...);
+ C is the scaled by N in Mode M and by (N-1) in mode D.
+ [C,N] = covm(...);
+ C is not scaled, provides the scaling factor N
+ C./N gives the scaled version.
+
+ see also: DECOVM, XCOVF
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ COVM generates covariance matrix
+ X and Y can contain missing values encoded wi
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+detrend
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 837
+ DETREND removes the trend from data, NaN's are considered as missing values
+
+ DETREND is fully compatible to previous Matlab and Octave DETREND with the following features added:
+ - handles NaN's by assuming that these are missing values
+ - handles unequally spaced data
+ - second output parameter gives the trend of the data
+ - compatible to Matlab and Octave
+
+ [...]=detrend([t,] X [,p])
+ removes trend for unequally spaced data
+ t represents the time points
+ X(i) is the value at time t(i)
+ p must be a scalar
+
+ [...]=detrend(X,0)
+ [...]=detrend(X,'constant')
+ removes the mean
+
+ [...]=detrend(X,p)
+ removes polynomial of order p (default p=1)
+
+ [...]=detrend(X,1) - default
+ [...]=detrend(X,'linear')
+ removes linear trend
+
+ [X,T]=detrend(...)
+
+ X is the detrended data
+ T is the removed trend
+
+ see also: SUMSKIPNAN, ZSCORE
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ DETREND removes the trend from data, NaN's are considered as missing values
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+durlev
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1241
+ function [AR,RC,PE] = durlev(ACF);
+ function [MX,PE] = durlev(ACF);
+ estimates AR(p) model parameter by solving the
+ Yule-Walker with the Durbin-Levinson recursion
+ for multiple channels
+ INPUT:
+ ACF Autocorrelation function from lag=[0:p]
+
+ OUTPUT
+ AR autoregressive model parameter
+ RC reflection coefficients (= -PARCOR coefficients)
+ PE remaining error variance
+ MX transformation matrix between ARP and RC (Attention: needs O(p^2) memory)
+ AR(:,K) = MX(:,K*(K-1)/2+(1:K));
+ RC(:,K) = MX(:,(1:K).*(2:K+1)/2);
+
+ All input and output parameters are organized in rows, one row
+ corresponds to the parameters of one channel
+
+ see also ACOVF ACORF AR2RC RC2AR LATTICE
+
+ REFERENCES:
+ Levinson N. (1947) "The Wiener RMS(root-mean-square) error criterion in filter design and prediction." J. Math. Phys., 25, pp.261-278.
+ Durbin J. (1960) "The fitting of time series models." Rev. Int. Stat. Inst. vol 28., pp 233-244.
+ P.J. Brockwell and R. A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+ S. Haykin "Adaptive Filter Theory" 3rd ed. Prentice Hall, 1996.
+ M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+ W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ function [AR,RC,PE] = durlev(ACF);
+ function [MX,PE] = durlev(ACF);
+ estimate
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 24
+flag_implicit_samplerate
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 135
+ The use of FLAG_IMPLICIT_SAMPLERATE is in experimental state.
+ FLAG_IMPLICIT_SAMPLERATE might even become obsolete.
+ Do not use it.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 62
+ The use of FLAG_IMPLICIT_SAMPLERATE is in experimental state.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 22
+flag_implicit_skip_nan
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 934
+ FLAG_IMPLICIT_SKIP_NAN sets and gets default mode for handling NaNs
+ 1 skips NaN's (the default mode if no mode is set)
+ 0 NaNs are propagated; input NaN's give NaN's at the output
+
+ FLAG = flag_implicit_skip_nan()
+ gets current mode
+
+ flag_implicit_skip_nan(FLAG)
+ sets mode
+
+ prevFLAG = flag_implicit_skip_nan(nextFLAG)
+ gets previous set FLAG and sets FLAG for the future
+ flag_implicit_skip_nan(prevFLAG)
+ resets FLAG to previous mode
+
+ It is used in:
+ SUMSKIPNAN, MEDIAN, QUANTILES, TRIMEAN
+ and affects many other functions like:
+ CENTER, KURTOSIS, MAD, MEAN, MOMENT, RMS, SEM, SKEWNESS,
+ STATISTIC, STD, VAR, ZSCORE etc.
+
+ The mode is stored in the global variable FLAG_implicit_skip_nan
+ It is recommended to use flag_implicit_skip_nan(1) as default and
+ flag_implicit_skip_nan(0) should be used for exceptional cases only.
+ This feature might disappear without further notice, so you should really not
+ rely on it.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ FLAG_IMPLICIT_SKIP_NAN sets and gets default mode for handling NaNs
+ 1 skips Na
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+flix
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 603
+ floating point index - interpolates data in case of non-integer indices
+
+ Y=flix(D,x)
+ FLIX returns Y=D(x) if x is an integer
+ otherwise D(x) is interpolated from the neighbors D(ceil(x)) and D(floor(x))
+
+ Applications:
+ (1) discrete Dataseries can be upsampled to higher sampling rate
+ (2) transformation of non-equidistant samples to equidistant samples
+ (3) [Q]=flix(sort(D),q*(length(D)+1)) calculates the q-quantile of data series D
+
+ FLIX(D,x) is the same as INTERP1(D,X,'linear'); Therefore, FLIX might
+ become obsolete in future.
+
+ see also: HIST2RES, Y2RES, PLOTCDF, INTERP1
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 73
+ floating point index - interpolates data in case of non-integer indices
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+histo
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 581
+ HISTO calculates histogram for each column
+ [H,X] = HISTO(Y,Mode)
+
+ Mode
+ 'rows' : frequency of each row
+ '1x' : single bin-values
+ 'nx' : separate bin-values for each column
+ X are the bin-values
+ H is the frequency of occurence of value X
+
+ HISTO(Y) with no output arguments:
+ plots the histogram bar(X,H)
+
+ more histogram-based results can be obtained by HIST2RES2
+
+ see also: HISTO, HISTO2, HISTO3, HISTO4
+
+ REFERENCE(S):
+ C.E. Shannon and W. Weaver "The mathematical theory of communication" University of Illinois Press, Urbana 1949 (reprint 1963).
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ HISTO calculates histogram for each column
+ [H,X] = HISTO(Y,Mode)
+
+ Mode
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+histo2
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1009
+ HISTO2 calculates histogram for multiple columns with separate bin values
+ for each data column.
+
+ R = HISTO2(Y)
+ R = HISTO2(Y, W)
+ Y data
+ W weight vector containing weights of each sample,
+ number of rows of Y and W must match.
+ default W=[] indicates that each sample is weighted with 1.
+
+ R = HISTO(...)
+ R is a struct with th fields
+ R.X the bin-values, bin-values are computed separately for each
+ data column, thus R.X is a matrix, each column contains the
+ the bin values of for each data column, unused elements are indicated with NaN.
+ In order to have common bin values, use HISTO3.
+ R.H is the frequency of occurence of value X
+ R.N are the number of valid (not NaN) samples (i.e. sum of weights)
+
+ more histogram-based results can be obtained by HIST2RES2
+
+ see also: HISTO, HISTO2, HISTO3, HISTO4
+
+ REFERENCE(S):
+ C.E. Shannon and W. Weaver "The mathematical theory of communication" University of Illinois Press, Urbana 1949 (reprint 1963).
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ HISTO2 calculates histogram for multiple columns with separate bin values
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+histo3
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1266
+ HISTO3 calculates histogram for multiple columns with common bin values
+ among all data columns, and can be useful for data compression.
+
+ R = HISTO3(Y)
+ R = HISTO3(Y, W)
+ Y data
+ W weight vector containing weights of each sample,
+ number of rows of Y and W must match.
+ default W=[] indicates that each sample is weighted with 1.
+ R struct with these fields
+ R.X the bin-values, bin-values are equal for each channel
+ thus R.X is a column vector. If bin values should
+ be computed separately for each data column, use HISTO2
+ R.H is the frequency of occurence of value X
+ R.N are the number of valid (not NaN) samples
+
+ Data compression can be performed in this way
+ [R,tix] = histo3(Y)
+ is the compression step
+
+ R.tix provides a compressed data representation.
+ R.compressionratio estimates the compression ratio
+
+ R.X(tix) and R.X(R.tix)
+ reconstruct the orginal signal (decompression)
+
+ The effort (in memory and speed) for compression is O(n*log(n)).
+ The effort (in memory and speed) for decompression is O(n) only.
+
+ see also: HISTO, HISTO2, HISTO3, HISTO4
+
+ REFERENCE(S):
+ C.E. Shannon and W. Weaver "The mathematical theory of communication" University of Illinois Press, Urbana 1949 (reprint 1963).
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ HISTO3 calculates histogram for multiple columns with common bin values
+ am
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+histo4
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 965
+ HISTO4 calculates histogram of multidimensional data samples
+ and supports data compression
+
+ R = HISTO4(Y)
+ R = HISTO4(Y, W)
+ Y data: on sample per row, each sample has with size(Y,2) elements
+ W weights of each sample (default: [])
+ W = [] indicates that each sample has equal weight
+ R is a struct with these fields:
+ R.X are the bin-values
+ R.H is the frequency of occurence of value X (weighted with W)
+ R.N are the total number of samples (or sum of W)
+
+ HISTO4 might be useful for data compression, because
+ [R,tix] = histo4(Y)
+ is the compression step
+ R.X(tix,:)
+ is the decompression step
+
+ The effort (in memory and speed) for compression is O(n*log(n))
+ The effort (in memory and speed) for decompression is only O(n)
+
+ see also: HISTO, HISTO2, HISTO3, HISTO4
+
+ REFERENCE(S):
+ C.E. Shannon and W. Weaver 'The mathematical theory of communication' University of Illinois Press, Urbana 1949 (reprint 1963).
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ HISTO4 calculates histogram of multidimensional data samples
+ and supports d
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+hup
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 588
+HUP(C) tests if the polynomial C is a Hurwitz-Polynomial.
+ It tests if all roots lie in the left half of the complex
+ plane
+ B=hup(C) is the same as
+ B=all(real(roots(c))<0) but much faster.
+ The Algorithm is based on the Routh-Scheme.
+ C are the elements of the Polynomial
+ C(1)*X^N + ... + C(N)*X + C(N+1).
+
+ HUP2 works also for multiple polynomials,
+ each row a poly - Yet not tested
+
+ REFERENCES:
+ F. Gausch "Systemtechnik", Textbook, University of Technology Graz, 1993.
+ Ch. Langraf and G. Schneider "Elemente der Regeltechnik", Springer Verlag, 1970.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 57
+HUP(C) tests if the polynomial C is a Hurwitz-Polynomial.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+invest0
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 842
+ First Investigation of a signal (time series) - automated part
+ [AutoCov,AutoCorr,ARPMX,E,ACFsd,NC]=invest0(Y,Pmax);
+
+ [AutoCov,AutoCorr,ARPMX,E,ACFsd,NC]=invest0(AutoCov,Pmax,Mode);
+
+
+ Y time series
+ Pmax maximal order (optional)
+
+ AutoCov Autocorrelation
+ AutoCorr normalized Autocorrelation
+ PartACF Partial Autocorrelation
+ ARPMX Autoregressive Parameter for order Pmax-1
+ E Error function E(p)
+ NC Number of values (length-missing values)
+
+ REFERENCES:
+ P.J. Brockwell and R.A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+ M.S. Grewal and A.P. Andrews "Kalman Filtering" Prentice Hall, 1993.
+ S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
+ M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+ W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ First Investigation of a signal (time series) - automated part
+ [AutoCov,AutoCo
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+invest1
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1306
+ First Investigation of a signal (time series) - interactive
+ [AutoCov,AutoCorr,ARPMX,E,CRITERIA,MOPS]=invest1(Y,Pmax,show);
+
+ Y time series
+ Pmax maximal order (optional)
+ show optional; if given the parameters are shown
+
+ AutoCov Autocorrelation
+ AutoCorr normalized Autocorrelation
+ PartACF Partial Autocorrelation
+ E Error function E(p)
+ CRITERIA curves of the various (see below) criteria,
+ MOPS=[optFPE optAIC optBIC optSBC optMDL optCAT optPHI];
+ optimal model order according to various criteria
+
+ FPE Final Prediction Error (Kay, 1987)
+ AIC Akaike Information Criterion (Marple, 1987)
+ BIC Bayesian Akaike Information Criterion (Wei, 1994)
+ SBC Schwartz's Bayesian Criterion (Wei, 1994)
+ MDL Minimal Description length Criterion (Marple, 1987)
+ CAT Parzen's CAT Criterion (Wei, 1994)
+ PHI Phi criterion (Pukkila et al. 1988)
+ minE order where E is minimal
+
+ REFERENCES:
+ P.J. Brockwell and R.A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+ S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
+ M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+ 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.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ First Investigation of a signal (time series) - interactive
+ [AutoCov,AutoCorr,
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+invfdemo
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 41
+ invfdemo demonstrates Inverse Filtering
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 41
+ invfdemo demonstrates Inverse Filtering
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+lattice
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1531
+ Estimates AR(p) model parameter with lattice algorithm (Burg 1968)
+ for multiple channels.
+ If you have the NaN-tools, LATTICE.M can handle missing values (NaN),
+
+ [...] = lattice(y [,Pmax [,Mode]]);
+
+ [AR,RC,PE] = lattice(...);
+ [MX,PE] = lattice(...);
+
+ INPUT:
+ y signal (one per row), can contain missing values (encoded as NaN)
+ Pmax max. model order (default size(y,2)-1))
+ Mode 'BURG' (default) Burg algorithm
+ 'GEOL' geometric lattice
+
+ OUTPUT
+ AR autoregressive model parameter
+ RC reflection coefficients (= -PARCOR coefficients)
+ PE remaining error variance
+ MX transformation matrix between ARP and RC (Attention: needs O(p^2) memory)
+ AR(:,K) = MX(:, K*(K-1)/2+(1:K)); = MX(:,sum(1:K-1)+(1:K));
+ RC(:,K) = MX(:,cumsum(1:K)); = MX(:,(1:K).*(2:K+1)/2);
+
+ All input and output parameters are organized in rows, one row
+ corresponds to the parameters of one channel
+
+ see also ACOVF ACORF AR2RC RC2AR DURLEV SUMSKIPNAN
+
+ REFERENCE(S):
+ J.P. Burg, "Maximum Entropy Spectral Analysis" Proc. 37th Meeting of the Society of Exp. Geophysiscists, Oklahoma City, OK 1967
+ J.P. Burg, "Maximum Entropy Spectral Analysis" PhD-thesis, Dept. of Geophysics, Stanford University, Stanford, CA. 1975.
+ P.J. Brockwell and R. A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+ S. Haykin "Adaptive Filter Theory" 3rd ed. Prentice Hall, 1996.
+ M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+ W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ Estimates AR(p) model parameter with lattice algorithm (Burg 1968)
+ for multip
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+lpc
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 759
+ LPC Linear prediction coefficients
+ The Burg-method is used to estimate the prediction coefficients
+
+ A = lpc(Y [,P]) finds the coefficients A=[ 1 A(2) ... A(N+1) ],
+ of an Pth order forward linear predictor
+
+ Xp(n) = -A(2)*X(n-1) - A(3)*X(n-2) - ... - A(N+1)*X(n-P)
+
+ such that the sum of the squares of the errors
+
+ err(n) = X(n) - Xp(n)
+
+ is minimized. X can be a vector or a matrix. If X is a matrix
+ containing a separate signal in each column, LPC returns a model
+ estimate for each column in the rows of A. N specifies the order
+ of the polynomial A(z).
+
+ If you do not specify a value for P, LPC uses a default P = length(X)-1.
+
+
+ see also ACOVF ACORF AR2POLY RC2AR DURLEV SUMSKIPNAN LATTICE
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ LPC Linear prediction coefficients
+ The Burg-method is used to estimate the pr
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+mvaar
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 784
+ Multivariate (Vector) adaptive AR estimation base on a multidimensional
+ Kalman filer algorithm. A standard VAR model (A0=I) is implemented. The
+ state vector is defined as X=(A1|A2...|Ap) and x=vec(X')
+
+ [x,e,Kalman,Q2] = mvaar(y,p,UC,mode,Kalman)
+
+ The standard MVAR model is defined as:
+
+ y(n)-A1(n)*y(n-1)-...-Ap(n)*y(n-p)=e(n)
+
+ The dimension of y(n) equals s
+
+ Input Parameters:
+
+ y Observed data or signal
+ p prescribed maximum model order (default 1)
+ UC update coefficient (default 0.001)
+ mode update method of the process noise covariance matrix 0...4 ^
+ correspond to S0...S4 (default 0)
+
+ Output Parameters
+
+ e prediction error of dimension s
+ x state vector of dimension s*s*p
+ Q2 measurement noise covariance matrix of dimension s x s
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ Multivariate (Vector) adaptive AR estimation base on a multidimensional
+ Kalman
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+mvar
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3018
+ MVAR estimates parameters of the Multi-Variate AutoRegressive model
+
+ Y(t) = Y(t-1) * A1 + ... + Y(t-p) * Ap + X(t);
+ whereas
+ Y(t) is a row vecter with M elements Y(t) = y(t,1:M)
+
+ Several estimation algorithms are implemented, all estimators
+ can handle data with missing values encoded as NaNs.
+
+ [AR,RC,PE] = mvar(Y, p);
+ [AR,RC,PE] = mvar(Y, p, Mode);
+
+ with
+ AR = [A1, ..., Ap];
+
+ INPUT:
+ Y Multivariate data series
+ p Model order
+ Mode determines estimation algorithm
+
+ OUTPUT:
+ AR multivariate autoregressive model parameter
+ RC reflection coefficients (= -PARCOR coefficients)
+ PE remaining error variances for increasing model order
+ PE(:,p*M+[1:M]) is the residual variance for model order p
+
+ All input and output parameters are organized in columns, one column
+ corresponds to the parameters of one channel.
+
+ Mode determines estimation algorithm.
+ 1: Correlation Function Estimation method using biased correlation function estimation method
+ also called the 'multichannel Yule-Walker' [1,2]
+ 6: Correlation Function Estimation method using unbiased correlation function estimation method
+
+ 2: Partial Correlation Estimation: Vieira-Morf [2] using unbiased covariance estimates.
+ In [1] this mode was used and (incorrectly) denominated as Nutall-Strand.
+ Its the DEFAULT mode; according to [1] it provides the most accurate estimates.
+ 5: Partial Correlation Estimation: Vieira-Morf [2] using biased covariance estimates.
+ Yields similar results than Mode=2;
+
+ 3: buggy: Partial Correlation Estimation: Nutall-Strand [2] (biased correlation function)
+ 9: Partial Correlation Estimation: Nutall-Strand [2] (biased correlation function)
+ 7: Partial Correlation Estimation: Nutall-Strand [2] (unbiased correlation function)
+ 8: Least Squares w/o nans in Y(t):Y(t-p)
+ 10: ARFIT [3]
+ 11: BURGV [4]
+ 13: modified BURGV -
+ 14: modified BURGV [4]
+ 15: Least Squares based on correlation matrix
+ 22: Modified Partial Correlation Estimation: Vieira-Morf [2,5] using unbiased covariance estimates.
+ 25: Modified Partial Correlation Estimation: Vieira-Morf [2,5] using biased covariance estimates.
+
+ 90,91,96: Experimental versions
+
+ Imputation methods:
+ 100+Mode:
+ 200+Mode: forward, past missing values are assumed zero
+ 300+Mode: backward, past missing values are assumed zero
+ 400+Mode: forward+backward, past missing values are assumed zero
+ 1200+Mode: forward, past missing values are replaced with predicted value
+ 1300+Mode: backward, 'past' missing values are replaced with predicted value
+ 1400+Mode: forward+backward, 'past' missing values are replaced with predicted value
+ 2200+Mode: forward, past missing values are replaced with predicted value + noise to prevent decaying
+ 2300+Mode: backward, past missing values are replaced with predicted value + noise to prevent decaying
+ 2400+Mode: forward+backward, past missing values are replaced with predicted value + noise to prevent decaying
+
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 70
+ MVAR estimates parameters of the Multi-Variate AutoRegressive model
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+mvfilter
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1028
+ Multi-variate filter function
+
+ Y = MVFILTER(B,A,X)
+ [Y,Z] = MVFILTER(B,A,X,Z)
+
+ Y = MVFILTER(B,A,X) filters the data in matrix X with the
+ filter described by cell arrays A and B to create the filtered
+ data Y. The filter is a 'Direct Form II Transposed'
+ implementation of the standard difference equation:
+
+ a0*Y(n) = b0*X(:,n) + b1*X(:,n-1) + ... + bq*X(:,n-q)
+ - a1*Y(:,n-1) - ... - ap*Y(:,n-p)
+
+ A=[a0,a1,a2,...,ap] and B=[b0,b1,b2,...,bq] must be matrices of
+ size Mx((p+1)*M) and Mx((q+1)*M), respectively.
+ a0,a1,...,ap, b0,b1,...,bq are matrices of size MxM
+ a0 is usually the identity matrix I or must be invertible
+ X should be of size MxN, if X has size NxM a warning
+ is raised, and the output Y is also transposed.
+
+ A simulated MV-AR process can be generiated with
+ Y = mvfilter(eye(M), [eye(M),-AR],randn(M,N));
+
+ A multivariate inverse filter can be realized with
+ [AR,RC,PE] = mvar(Y,P);
+ E = mvfilter([eye(M),-AR],eye(M),Y);
+
+ see also: MVAR, FILTER
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 31
+ Multi-variate filter function
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+mvfreqz
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3844
+ MVFREQZ multivariate frequency response
+ [S,h,PDC,COH,DTF,DC,pCOH,dDTF,ffDTF,pCOH2,PDCF,coh,GGC,Af,GPDC] = mvfreqz(B,A,C,f,Fs)
+ [...] = mvfreqz(B,A,C,N,Fs)
+
+ INPUT:
+ =======
+ A, B multivariate polynomials defining the transfer function
+
+ a0*Y(n) = b0*X(n) + b1*X(n-1) + ... + bq*X(n-q)
+ - a1*Y(n-1) - ... - ap*Y(:,n-p)
+
+ A=[a0,a1,a2,...,ap] and B=[b0,b1,b2,...,bq] must be matrices of
+ size Mx((p+1)*M) and Mx((q+1)*M), respectively.
+
+ C is the covariance of the input noise X (i.e. D'*D if D is the mixing matrix)
+ N if scalar, N is the number of frequencies
+ if N is a vector, N are the designated frequencies.
+ Fs sampling rate [default 2*pi]
+
+ A,B,C and D can by obtained from a multivariate time series
+ through the following commands:
+ [AR,RC,PE] = mvar(Y,P);
+ M = size(AR,1); % number of channels
+ A = [eye(M),-AR];
+ B = eye(M);
+ C = PE(:,M*P+1:M*(P+1));
+
+ Fs sampling rate in [Hz]
+ (N number of frequencies for computing the spectrum, this will become OBSOLETE),
+ f vector of frequencies (in [Hz])
+
+
+ OUTPUT:
+ =======
+ S power spectrum
+ h transfer functions, abs(h.^2) is the non-normalized DTF [11]
+ PDC partial directed coherence [2]
+ DC directed coupling
+ COH coherency (complex coherence) [5]
+ DTF directed transfer function
+ pCOH partial coherence
+ dDTF direct Directed Transfer function
+ ffDTF full frequency Directed Transfer Function
+ pCOH2 partial coherence - alternative method
+ GGC a modified version of Geweke's Granger Causality [Geweke 1982]
+ !!! it uses a Multivariate AR model, and computes the bivariate GGC as in [Bressler et al 2007].
+ This is not the same as using bivariate AR models and GGC as in [Bressler et al 2007]
+ Af Frequency transform of A(z), abs(Af.^2) is the non-normalized PDC [11]
+ PDCF Partial Directed Coherence Factor [2]
+ GPDC Generalized Partial Directed Coherence [9,10]
+
+ see also: FREQZ, MVFILTER, MVAR
+
+ REFERENCE(S):
+ [1] H. Liang et al. Neurocomputing, 32-33, pp.891-896, 2000.
+ [2] L.A. Baccala and K. Samashima, Biol. Cybern. 84,463-474, 2001.
+ [3] A. Korzeniewska, et al. Journal of Neuroscience Methods, 125, 195-207, 2003.
+ [4] Piotr J. Franaszczuk, Ph.D. and Gregory K. Bergey, M.D.
+ Fast Algorithm for Computation of Partial Coherences From Vector Autoregressive Model Coefficients
+ World Congress 2000, Chicago.
+ [5] Nolte G, Bai O, Wheaton L, Mari Z, Vorbach S, Hallett M.
+ Identifying true brain interaction from EEG data using the imaginary part of coherency.
+ Clin Neurophysiol. 2004 Oct;115(10):2292-307.
+ [6] Schlogl A., Supp G.
+ Analyzing event-related EEG data with multivariate autoregressive parameters.
+ (Eds.) C. Neuper and W. Klimesch,
+ Progress in Brain Research: Event-related Dynamics of Brain Oscillations.
+ Analysis of dynamics of brain oscillations: methodological advances. Elsevier.
+ Progress in Brain Research 159, 2006, p. 135 - 147
+ [7] Bressler S.L., Richter C.G., Chen Y., Ding M. (2007)
+ Cortical fuctional network organization from autoregressive modelling of loal field potential oscillations.
+ Statistics in Medicine, doi: 10.1002/sim.2935
+ [8] Geweke J., 1982
+ J.Am.Stat.Assoc., 77, 304-313.
+ [9] L.A. Baccala, D.Y. Takahashi, K. Sameshima. (2006)
+ Generalized Partial Directed Coherence.
+ Submitted to XVI Congresso Brasileiro de Automatica, Salvador, Bahia.
+ [10] L.A. Baccala, D.Y. Takahashi, K. Sameshima.
+ Computer Intensive Testing for the Influence Between Time Series,
+ Eds. B. Schelter, M. Winterhalder, J. Timmer:
+ Handbook of Time Series Analysis - Recent Theoretical Developments and Applications
+ Wiley, p.413, 2006.
+ [11] M. Eichler
+ On the evaluation of informatino flow in multivariate systems by the directed transfer function
+ Biol. Cybern. 94: 469-482, 2006.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ MVFREQZ multivariate frequency response
+ [S,h,PDC,COH,DTF,DC,pCOH,dDTF,ffDTF,pC
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+pacf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 137
+ Partial Autocorrelation function
+ [parcor,sig,cil,ciu] = pacf(Z,N);
+
+ Input:
+ Z Signal, each row is analysed
+ N # of coefficients
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 69
+ Partial Autocorrelation function
+ [parcor,sig,cil,ciu] = pacf(Z,N);
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+parcor
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1160
+ estimates partial autocorrelation coefficients
+ Multiple channels can be used (one per row).
+
+ [PARCOR, AR, PE] = parcor(AutoCov); % calculates Partial autocorrelation, autoregressive coefficients and residual error variance from the Autocorrelation function.
+
+ [PARCOR] = parcor(acovf(x,p)); % calculates the Partial Autocorrelation coefficients of the data series x up to order p
+
+ INPUT:
+ AutoCov Autocorrelation function for lag=0:P
+
+ OUTPUT
+ AR autoregressive model parameter
+ PARCOR partial correlation coefficients (= -reflection coefficients)
+ PE remaining error variance
+
+ All input and output parameters are organized in rows, one row
+ corresponds to the parameters of one channel.
+ The PARCOR coefficients are the negative reflection coefficients.
+ A significance test is implemented in PACF.
+
+ see also: PACF ACOVF ACORF DURLEV AC2RC
+
+ REFERENCES:
+ P.J. Brockwell and R.A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+ S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
+ M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+ W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ estimates partial autocorrelation coefficients
+ Multiple channels can be used
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+poly2ac
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 183
+ converts an AR polynomial into an autocorrelation sequence
+ [R] = poly2ac(a [,efinal] );
+
+ see also ACOVF ACORF AR2RC RC2AR DURLEV AC2POLY, POLY2RC, RC2POLY, RC2AC, AC2RC, POLY2AC
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ converts an AR polynomial into an autocorrelation sequence
+ [R] = poly2ac(a [,e
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+poly2ar
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 288
+ Converts AR polymials into autoregressive parameters.
+ Multiple polynomials can be converted.
+
+ function [AR] = poly2ar(A);
+
+ INPUT:
+ A AR polynomial, each row represents one polynomial
+
+ OUTPUT
+ AR autoregressive model parameter
+
+ see also ACOVF ACORF DURLEV RC2AR AR2POLY
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 54
+ Converts AR polymials into autoregressive parameters.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+poly2rc
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 434
+ converts AR-polynomial into reflection coefficients
+ [RC,R0] = poly2rc(A [,Efinal])
+
+ INPUT:
+ A AR polynomial, each row represents one polynomial
+ Efinal is the final prediction error variance (default value 1)
+
+ OUTPUT
+ RC reflection coefficients
+ R0 is the variance (autocovariance at lag=0) based on the
+ prediction error
+
+
+ see also ACOVF ACORF AR2RC RC2AR DURLEV AC2POLY, POLY2RC, RC2POLY, RC2AC, AC2RC, POLY2AC
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ converts AR-polynomial into reflection coefficients
+ [RC,R0] = poly2rc(A [,Efin
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+rc2ac
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 176
+ converts reflection coefficients to autocorrelation sequence
+ [R] = rc2ac(RC,R0);
+
+ see also ACOVF ACORF AR2RC RC2AR DURLEV AC2POLY, POLY2RC, RC2POLY, RC2AC, AC2RC, POLY2AC
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ converts reflection coefficients to autocorrelation sequence
+ [R] = rc2ac(RC,R0
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+rc2ar
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1000
+ converts reflection coefficients into autoregressive parameters
+ uses the Durbin-Levinson recursion for multiple channels
+ function [AR,RC,PE,ACF] = rc2ar(RC);
+ function [MX,PE] = rc2ar(RC);
+
+ INPUT:
+ RC reflection coefficients
+
+ OUTPUT
+ AR autoregressive model parameter
+ RC reflection coefficients (= -PARCOR coefficients)
+ PE remaining error variance (relative to PE(1)=1)
+ MX transformation matrix between ARP and RC (Attention: needs O(p^2) memory)
+ arp=MX(:,K*(K-1)/2+(1:K));
+ rc =MX(:,(1:K).*(2:K+1)/2);
+
+ All input and output parameters are organized in rows, one row
+ corresponds to the parameters of one channel
+
+ see also ACOVF ACORF DURLEV AR2RC
+
+ REFERENCES:
+ P.J. Brockwell and R. A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+ S. Haykin "Adaptive Filter Theory" 3rd ed. Prentice Hall, 1996.
+ M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+ W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ converts reflection coefficients into autoregressive parameters
+ uses the Durbi
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+rc2poly
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 174
+ converts reflection coefficients into an AR-polynomial
+ [a,efinal] = rc2poly(K)
+
+ see also ACOVF ACORF AR2RC RC2AR DURLEV AC2POLY, POLY2RC, RC2POLY, RC2AC, AC2RC, POLY2AC
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ converts reflection coefficients into an AR-polynomial
+ [a,efinal] = rc2poly(K)
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+rmle
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 432
+ RMLE estimates AR Parameters using the Recursive Maximum Likelihood
+ Estimator according to [1]
+
+ Use: [a,VAR]=rmle(x,p)
+ Input:
+ x is a column vector of data
+ p is the model order
+ Output:
+ a is a vector with the AR parameters of the recursive MLE
+ VAR is the excitation white noise variance estimate
+
+ Reference(s):
+ [1] Kay S.M., Modern Spectral Analysis - Theory and Applications.
+ Prentice Hall, p. 232-233, 1988.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ RMLE estimates AR Parameters using the Recursive Maximum Likelihood
+ Estimator
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+sbispec
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 26
+ SBISPEC show BISPECTRUM
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 26
+ SBISPEC show BISPECTRUM
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+selmo
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2179
+ Model order selection of an autoregrssive model
+ [FPE,AIC,BIC,SBC,MDL,CAT,PHI,optFPE,optAIC,optBIC,optSBC,optMDL,optCAT,optPHI]=selmo(E,N);
+
+ E Error function E(p)
+ N length of the data set, that was used for calculating E(p)
+ show optional; if given the parameters are shown
+
+ FPE Final Prediction Error (Kay 1987, Wei 1990, Priestley 1981 -> Akaike 1969)
+ AIC Akaike Information Criterion (Marple 1987, Wei 1990, Priestley 1981 -> Akaike 1974)
+ BIC Bayesian Akaike Information Criterion (Wei 1990, Priestley 1981 -> Akaike 1978,1979)
+ CAT Parzen's CAT Criterion (Wei 1994 -> Parzen 1974)
+ MDL Minimal Description length Criterion (Marple 1987 -> Rissanen 1978,83)
+ SBC Schwartz's Bayesian Criterion (Wei 1994; Schwartz 1978)
+ PHI Phi criterion (Pukkila et al. 1988, Hannan 1980 -> Hannan & Quinn, 1979)
+ HAR Haring G. (1975)
+ JEW Jenkins and Watts (1968)
+
+ optFPE order where FPE is minimal
+ optAIC order where AIC is minimal
+ optBIC order where BIC is minimal
+ optSBC order where SBC is minimal
+ optMDL order where MDL is minimal
+ optCAT order where CAT is minimal
+ optPHI order where PHI is minimal
+
+ usually is
+ AIC > FPE > *MDL* > PHI > SBC > CAT ~ BIC
+
+ REFERENCES:
+ P.J. Brockwell and R.A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+ S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
+ M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+ 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.
+ Jenkins G.M. Watts D.G "Spectral Analysis and its applications", Holden-Day, 1968.
+ G. Haring "Über die Wahl der optimalen Modellordnung bei der Darstellung von stationären Zeitreihen mittels Autoregressivmodell als Basis der Analyse von EEG - Biosignalen mit Hilfe eines Digitalrechners", Habilitationschrift - Technische Universität Graz, Austria, 1975.
+ (1)"About selecting the optimal model at the representation of stationary time series by means of an autoregressive model as basis of the analysis of EEG - biosignals by means of a digital computer)"
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ Model order selection of an autoregrssive model
+ [FPE,AIC,BIC,SBC,MDL,CAT,PHI,o
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+selmo2
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 271
+ SELMO2 - model order selection for univariate and multivariate
+ autoregressive models
+
+ X = selmo(y,Pmax);
+
+ y data series
+ Pmax maximum model order
+ X.A, X.B, X.C parameters of AR model
+ X.OPT... various optimization criteria
+
+ see also: SELMO, MVAR,
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ SELMO2 - model order selection for univariate and multivariate
+ autoregressi
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+sinvest1
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 93
+SINVEST1 shows the parameters of a time series calculated by INVEST1
+ only called by INVEST1
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+SINVEST1 shows the parameters of a time series calculated by INVEST1
+ only calle
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 10
+sumskipnan
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1234
+ SUMSKIPNAN adds all non-NaN values.
+
+ All NaN's are skipped; NaN's are considered as missing values.
+ SUMSKIPNAN of NaN's only gives O; and the number of valid elements is return.
+ SUMSKIPNAN is also the elementary function for calculating
+ various statistics (e.g. MEAN, STD, VAR, RMS, MEANSQ, SKEWNESS,
+ KURTOSIS, MOMENT, STATISTIC etc.) from data with missing values.
+ SUMSKIPNAN implements the DIMENSION-argument for data with missing values.
+ Also the second output argument return the number of valid elements (not NaNs)
+
+ Y = sumskipnan(x [,DIM])
+ [Y,N,SSQ] = sumskipnan(x [,DIM])
+ [...] = sumskipnan(x, DIM, W)
+
+ x input data
+ DIM dimension (default: [])
+ empty DIM sets DIM to first non singleton dimension
+ W weight vector for weighted sum, numel(W) must fit size(x,DIM)
+ Y resulting sum
+ N number of valid (not missing) elements
+ SSQ sum of squares
+
+ the function FLAG_NANS_OCCURED() returns whether any value in x
+ is a not-a-number (NaN)
+
+ features:
+ - can deal with NaN's (missing values)
+ - implements dimension argument.
+ - computes weighted sum
+ - compatible with Matlab and Octave
+
+ see also: FLAG_NANS_OCCURED, SUM, NANSUM, MEAN, STD, VAR, RMS, MEANSQ,
+ SSQ, MOMENT, SKEWNESS, KURTOSIS, SEM
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 36
+ SUMSKIPNAN adds all non-NaN values.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+tsademo
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 42
+ TSADEMO demonstrates INVEST1 on EEG data
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 42
+ TSADEMO demonstrates INVEST1 on EEG data
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+ucp
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 476
+ UCP(C) tests if the polynomial C is a Unit-Circle-Polynomial.
+ It tests if all roots lie inside the unit circle like
+ B=ucp(C) does the same as
+ B=all(abs(roots(C))<1) but much faster.
+ The Algorithm is based on the Jury-Scheme.
+ C are the elements of the Polynomial
+ C(1)*X^N + ... + C(N)*X + C(N+1).
+
+ REFERENCES:
+ O. Foellinger "Lineare Abtastsysteme", Oldenburg Verlag, Muenchen, 1986.
+ F. Gausch "Systemtechnik", Textbook, University of Technology Graz, 1993.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 62
+ UCP(C) tests if the polynomial C is a Unit-Circle-Polynomial.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+y2res
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 534
+ Y2RES evaluates basic statistics of a data series
+
+ R = y2res(y)
+ several statistics are estimated from each column of y
+
+ OUTPUT:
+ R.N number of samples, NaNs are not counted
+ R.SUM sum of samples
+ R.MEAN mean
+ R.STD standard deviation
+ R.VAR variance
+ R.Max Maximum
+ R.Min Minimum
+ ... and many more including:
+ MEDIAN, Quartiles, Variance, standard error of the mean (SEM),
+ Coefficient of Variation, Quantization (QUANT), TRIMEAN, SKEWNESS,
+ KURTOSIS, Root-Mean-Square (RMS), ENTROPY
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ Y2RES evaluates basic statistics of a data series
+
+ R = y2res(y)
+ several stat
+
+
+
+
+
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff