tsa

Stochastic concepts and maximum entropy methods for time series analysis

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Univariate (stationary) analysis

acovf
ACOVF estimates autocovariance function (not normalized) NaN's are interpreted as missing values.
acorf
Calculates autocorrelations for multiple data series.
biacovf
BiAutoCovariance function [BiACF] = biacovf(Z,N);
bispec
Calculates Bispectrum [BISPEC] = bispec(Z,N);
durlev
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:
lattice
Estimates AR(p) model parameter with lattice algorithm (Burg 1968) for multiple channels.
rmle
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
pacf
Partial Autocorrelation function [parcor,sig,cil,ciu] = pacf(Z,N);
parcor
estimates partial autocorrelation coefficients Multiple channels can be used (one per row).
invest0
First Investigation of a signal (time series) - automated part [AutoCov,AutoCorr,ARPMX,E,ACFsd,NC]=invest0(Y,Pmax);
invest1
First Investigation of a signal (time series) - interactive [AutoCov,AutoCorr,ARPMX,E,CRITERIA,MOPS]=invest1(Y,Pmax,show);
selmo
Model order selection of an autoregrssive model [FPE,AIC,BIC,SBC,MDL,CAT,PHI,optFPE,optAIC,optBIC,optSBC,optMDL,optCAT,optPHI]=selmo(E,N);
selmo2
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 mode
hup
HUP(C) tests if the polynomial C is a Hurwitz-Polynomial.
ucp
UCP(C) tests if the polynomial C is a Unit-Circle-Polynomial.
y2res
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
ar_spa
AR_SPA decomposes an AR-spectrum into its compontents [w,A,B,R,P,F,ip] = ar_spa(AR,fs,E);
flix
floating point index - interpolates data in case of non-integer indices

Multivariate stationary analysis

mvar
MVAR estimates parameters of the Multi-Variate AutoRegressive model
mvfilter
Multi-variate filter function
mvfreqz
MVFREQZ multivariate frequency response [S,h,PDC,COH,DTF,DC,pCOH,dDTF,ffDTF,pCOH2,PDCF,coh,GGC,Af,GPDC,GGC2,DCOH] = mvfreqz(B,A,C,f,Fs) [...] = mvfreqz(B,A,C,N,Fs) INPUT: ======= A, B mult
arfit2
ARFIT2 estimates multivariate autoregressive parameters of the MVAR process Y

Adaptive (time-varying) analysis

aar
Calculates adaptive autoregressive (AAR) and adaptive autoregressive moving average estimates (AARMA) of real-valued data series using Kalman filter algorithm.
aarmam
Estimating Adaptive AutoRegressive-Moving-Average-and-mean model (includes mean term)
adim
ADIM adaptive information matrix.
amarma
Adaptive Mean-AutoRegressive-Moving-Average model estimation [z,e,ESU,REV,V,Z,SPUR] = amarma(y, mode, MOP, UC, z0, Z0, V0, W);
mvaar
Multivariate (Vector) adaptive AR estimation base on a multidimensional Kalman filer algorithm.

Conversions between forms

ac2poly
converts the autocorrelation sequence into an AR polynomial [A,Efinal] = ac2poly(r)
ac2rc
converts the autocorrelation function into reflection coefficients [RC,r0] = ac2rc(r)
ar2rc
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);
rc2ar
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);
poly2ac
converts an AR polynomial into an autocorrelation sequence [R] = poly2ac(a [,efinal] );
poly2ar
Converts AR polymials into autoregressive parameters.
poly2rc
converts AR-polynomial into reflection coefficients [RC,R0] = poly2rc(A [,Efinal])
rc2ac
converts reflection coefficients to autocorrelation sequence [R] = rc2ac(RC,R0);
rc2poly
converts reflection coefficients into an AR-polynomial [a,efinal] = rc2poly(K)
ar2poly
converts autoregressive parameters into AR polymials Multiple polynomials can be converted.

Utility functions

arcext
ARCEXT extracts AR and RC of order P from Matrix MX function [AR,RC] = arcext(MX,P);
sinvest1
SINVEST1 shows the parameters of a time series calculated by INVEST1 only called by INVEST1
sbispec
SBISPEC show BISPECTRUM
flag_implicit_samplerate
The use of FLAG_IMPLICIT_SAMPLERATE is in experimental state.

Test suites

tsademo
TSADEMO demonstrates INVEST1 on EEG data
bisdemo
BISDEMO (script) Shows BISPECTRUM of eeg8s.mat
invfdemo
invfdemo demonstrates Inverse Filtering

Package: tsa