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/

- detrend DETREND removes the trend from data, NaN's are considered as missing values

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