/usr/share/octave/packages/tsa-4.2.7/aar.m is in octave-tsa 4.2.7-1build1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 | function [a,e,REV,TOC,CPUTIME,ESU] = aar(y, Mode, arg3, arg4, arg5, arg6, arg7, arg8, arg9);
% 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://pub.ist.ac.at/~schloegl/publications/
%
% $Id: aar.m 11693 2013-03-04 06:40:14Z schloegl $
% Copyright (C) 1998-2003 by Alois Schloegl <a.schloegl@ieee.org>
%
% 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/>.
[nc,nr]=size(y);
%if nc<nr y=y'; end; tmp=nr;nc=nr; nr=tmp;end;
if nargin<2 Mode=0; end;
% check Mode (argument2)
if prod(size(Mode))==2
aMode=Mode(1);
vMode=Mode(2);
end;
if any(aMode==(0:14)) && any(vMode==(0:7)),
fprintf(1,['a' int2str(aMode) 'e' int2str(vMode) ' ']);
else
fprintf(2,'Error AAR.M: invalid Mode argument\n');
return;
end;
% check model order (argument3)
if nargin<3 MOP=[10,0]; else MOP= arg3; end;
if length(MOP)==0 p=10; q=0; MOP=p;
elseif length(MOP)==1 p=MOP(1); q=0; MOP=p;
elseif length(MOP)>=2 p=MOP(1); q=MOP(2); MOP=p+q;
end;
if nargin<4 UC=0; else UC= arg4; end;
a0=zeros(1,MOP);
A0=eye(MOP);
if nargin>4,
if all(size(arg5)==([1,1]*(MOP+1))); % extended covariance matrix of AAR parameters
a0 = arg5(1,2:size(arg5,2));
A0 = arg5(2:size(arg5,1),2:size(arg5,2)) - a0'*a0;
else
a0 = arg5;
if nargin>5
A0 = arg6;
end;
end;
end;
if nargin<7, W = []; else W = arg7; end;
if all(size(W)==MOP),
if aMode ~= 0,
fprintf(1,'aMode should be 0, because W is given.\n');
end;
elseif isempty(W),
if aMode == 0,
fprintf(1,'aMode must be non-zero, because W is not given.\n');
end;
elseif any(size(W)~=MOP),
fprintf(1,'size of W does not fit. It must be %i x %i.\n',MOP,MOP);
return;
end;
if nargin<8, V0 = []; else V0 = arg8; end;
if all(size(V0)==nr),
if vMode ~= 0,
fprintf(1,'vMode should be 0, because V is given.\n');
end;
elseif isempty(V0),
if aMode == 0,
fprintf(1,'vMode must be non-zero, because V is not given.\n');
end;
else
fprintf(1,'size of V does not fit. It must be 1x1.\n');
return;
end;
% if nargin<7 TH=3; else TH = arg7; end;
% TH=TH*var(y);
% TH=TH*mean(detrend(y,0).^2);
MSY=mean(detrend(y,0).^2);
e=zeros(nc,1);
Q=zeros(nc,1);
V=zeros(nc,1);
T=zeros(nc,1);
%DET=zeros(nc,1);
SPUR=zeros(nc,1);
ESU=zeros(nc,1);
a=a0(ones(nc,1),:);
%a=zeros(nc,MOP);
%b=zeros(nc,q);
mu=1-UC; % Patomaeki 1995
lambda=(1-UC); % Schloegl 1996
arc=poly((1-UC*2)*[1;1]);b0=sum(arc); % Whale forgettting factor for Mode=258,(Bianci et al. 1997)
dW=UC/MOP*eye(MOP); % Schloegl
%------------------------------------------------
% First Iteration
%------------------------------------------------
Y=zeros(MOP,1);
C=zeros(MOP);
%X=zeros(q,1);
at=a0;
A=A0;
E=y(1);
e(1)=E;
if ~isempty(V0)
V(1) = V0;
else
V(1) = (1-UC) + UC*E*E;
end;
ESU(1) = 1; %Y'*A*Y;
A1=zeros(MOP);A2=A1;
tic;CPUTIME=cputime;
%------------------------------------------------
% Update Equations
%------------------------------------------------
T0=2;
for t=T0:nc,
%Y=[y(t-1); Y(1:p-1); E ; Y(p+1:MOP-1)]
if t<=p Y(1:t-1)=y(t-1:-1:1); % Autoregressive
else Y(1:p)=y(t-1:-1:t-p);
end;
if t<=q Y(p+(1:t-1))=e(t-1:-1:1); % Moving Average
else Y(p+1:MOP)=e(t-1:-1:t-q);
end;
% Prediction Error
E = y(t) - a(t-1,:)*Y;
e(t) = E;
E2=E*E;
AY=A*Y;
esu=Y'*AY;
ESU(t)=esu;
if isnan(E),
a(t,:)=a(t-1,:);
else
V(t) = V(t-1)*(1-UC)+UC*E2;
if aMode == -1, % LMS
% V(t) = V(t-1)*(1-UC)+UC*E2;
a(t,:)=a(t-1,:) + (UC/MSY)*E*Y';
elseif aMode == -2, % LMS with adaptive estimation of the variance
a(t,:)=a(t-1,:) + UC/V(t)*E*Y';
else % Kalman filtering (including RLS)
if vMode==0, %eMode==4
Q(t) = (esu + V0);
elseif vMode==1, %eMode==4
Q(t) = (esu + V(t));
elseif vMode==2, %eMode==2
Q(t) = (esu + 1);
elseif vMode==3, %eMode==3
Q(t) = (esu + lambda);
elseif vMode==4, %eMode==1
Q(t) = (esu + V(t-1));
elseif vMode==5, %eMode==6
if E2>esu
V(t)=(1-UC)*V(t-1)+UC*(E2-esu);
else
V(t)=V(t-1);
end;
Q(t) = (esu + V(t));
elseif vMode==6, %eMode==7
if E2>esu
V(t)=(1-UC)*V(t-1)+UC*(E2-esu);
else
V(t)=V(t-1);
end;
Q(t) = (esu + V(t-1));
elseif vMode==7, %eMode==8
Q(t) = esu;
end;
k = AY / Q(t); % Kalman Gain
a(t,:) = a(t-1,:) + k'*E;
if aMode==0, %AMode=0
A = A - k*AY' + W; % Schloegl et al. 2003
elseif aMode==1, %AMode=1
A = (1+UC)*(A - k*AY'); % Schloegl et al. 1997
elseif aMode==2, %AMode=11
A = A - k*AY';
A = A + sum(diag(A))*dW;
elseif aMode==3, %AMode=5
A = A - k*AY' + sum(diag(A))*dW;
elseif aMode==4, %AMode=6
A = A - k*AY' + UC*eye(MOP); % Schloegl 1998
elseif aMode==5, %AMode=2
A = A - k*AY' + UC*UC*eye(MOP);
elseif aMode==6, %AMode=2
T(t)=(1-UC)*T(t-1)+UC*(E2-Q(t))/(Y'*Y);
A=A*V(t-1)/Q(t);
if T(t)>0 A=A+T(t)*eye(MOP); end;
elseif aMode==7, %AMode=6
T(t)=(1-UC)*T(t-1)+UC*(E2-Q(t))/(Y'*Y);
A=A*V(t)/Q(t);
if T(t)>0 A=A+T(t)*eye(MOP); end;
elseif aMode==8, %AMode=5
Q_wo = (Y'*C*Y + V(t-1));
C=A-k*AY';
T(t)=(1-UC)*T(t-1)+UC*(E2-Q_wo)/(Y'*Y);
if T(t)>0 A=C+T(t)*eye(MOP); else A=C; end;
elseif aMode==9, %AMode=3
A = A - (1+UC)*k*AY';
A = A + sum(diag(A))*dW;
elseif aMode==10, %AMode=7
A = A - (1+UC)*k*AY' + sum(diag(A))*dW;
elseif aMode==11, %AMode=8
A = A - (1+UC)*k*AY' + UC*eye(MOP); % Schloegl 1998
elseif aMode==12, %AMode=4
A = A - (1+UC)*k*AY' + UC*UC*eye(MOP);
elseif aMode==13
A = A - k*AY' + UC*diag(diag(A));
elseif aMode==14
A = A - k*AY' + (UC*UC)*diag(diag(A));
end;
end;
end;
end;
%a=a(end,:);
TOC = toc;
CPUTIME = cputime - CPUTIME;
%REV = (e'*e)/(y'*y);
REV = mean(e.*e)./mean(y.*y);
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