318 lines
17 KiB
HTML
318 lines
17 KiB
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<title>Description of DiffuseKalmanSmoother3</title>
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<meta name="description" content="function [a,etahat,a1, aK] = DiffuseKalmanSmoother3(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)">
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<div><a href="../index.html">Home</a> > <a href="index.html">.</a> > DiffuseKalmanSmoother3.m</div>
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<!--<table width="100%"><tr><td align="left"><a href="../index.html"><img alt="<" border="0" src="../left.png"> Master index</a></td>
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<td align="right"><a href="index.html">Index for . <img alt=">" border="0" src="../right.png"></a></td></tr></table>-->
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<h1>DiffuseKalmanSmoother3
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</h1>
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<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="box"><strong>function [a,etahat,a1, aK] = DiffuseKalmanSmoother3(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)</strong></div>
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<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="box"><strong>function [alphahat,etahat,a1, aK] = DiffuseKalmanSmoother3(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf) </strong></div>
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<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="fragment"><pre class="comment">function [a,etahat,a1, aK] = DiffuseKalmanSmoother3(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)
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Modified by M. Ratto
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New output argument aK: 1-step to nk-stpe ahed predictions)
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New input argument nk: max order of predictions in aK
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New option options_.diffuse_d where the DKF stops (common with
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diffuselikelihood3)
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New icc variable to count number of iterations for Finf steps
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Pstar % Pinf simmetric
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New termination of DKF iterations based on options_.diffuse_d
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Li also stored during DKF iterations !!
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some bugs corrected in the DKF part of the smoother (Z matrix and
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alphahat)
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stephane.adjemian@cepremap.cnrs.fr [09-16-2004]
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See "Fast Filtering and Smoothing for Multivariate State Space
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Models", S.J. Koopman and J. Durbin (2000, in Journal of Time Series
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Analysis, vol. 21(3), pp. 281-296).</pre></div>
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<!-- crossreference -->
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<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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This function calls:
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<ul style="list-style-image:url(../matlabicon.gif)">
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<li><a href="steady.html" class="code" title="function steady(linear)">steady</a> Copyright (C) 2001 Michel Juillard</li></ul>
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This function is called by:
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<ul style="list-style-image:url(../matlabicon.gif)">
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<li><a href="DsgeSmoother.html" class="code" title="function [alphahat,etahat,epsilonhat,ahat,SteadyState,trend_coeff,aK] = DsgeSmoother(xparam1,gend,Y)">DsgeSmoother</a> stephane.adjemian@cepremap.cnrs.fr [09-07-2004]</li></ul>
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<!-- crossreference -->
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<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="fragment"><pre>0001 <a name="_sub0" href="#_subfunctions" class="code">function [alphahat,etahat,a1, aK] = DiffuseKalmanSmoother3(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)</a>
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0002 <span class="comment">%function [a,etahat,a1, aK] = DiffuseKalmanSmoother3(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)</span>
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0003 <span class="comment">% Modified by M. Ratto</span>
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0004 <span class="comment">% New output argument aK: 1-step to nk-stpe ahed predictions)</span>
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0005 <span class="comment">% New input argument nk: max order of predictions in aK</span>
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0006 <span class="comment">% New option options_.diffuse_d where the DKF stops (common with</span>
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0007 <span class="comment">% diffuselikelihood3)</span>
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0008 <span class="comment">% New icc variable to count number of iterations for Finf steps</span>
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0009 <span class="comment">% Pstar % Pinf simmetric</span>
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0010 <span class="comment">% New termination of DKF iterations based on options_.diffuse_d</span>
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0011 <span class="comment">% Li also stored during DKF iterations !!</span>
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0012 <span class="comment">% some bugs corrected in the DKF part of the smoother (Z matrix and</span>
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0013 <span class="comment">% alphahat)</span>
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0014 <span class="comment">%</span>
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0015 <span class="comment">% stephane.adjemian@cepremap.cnrs.fr [09-16-2004]</span>
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0016 <span class="comment">%</span>
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0017 <span class="comment">% See "Fast Filtering and Smoothing for Multivariate State Space</span>
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0018 <span class="comment">% Models", S.J. Koopman and J. Durbin (2000, in Journal of Time Series</span>
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0019 <span class="comment">% Analysis, vol. 21(3), pp. 281-296).</span>
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0020
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0021 <span class="keyword">global</span> options_
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0022
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0023 nk = options_.nk;
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0024 spinf = size(Pinf1);
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0025 spstar = size(Pstar1);
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0026 v = zeros(pp,smpl);
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0027 a = zeros(mm,smpl+1);
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0028 a1 = a;
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0029 aK = zeros(nk,mm,smpl+nk);
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0030 Fstar = zeros(pp,smpl);
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0031 Finf = zeros(pp,smpl);
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0032 Ki = zeros(mm,pp,smpl);
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0033 Li = zeros(mm,mm,pp,smpl);
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0034 Linf = zeros(mm,mm,pp,smpl);
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0035 L0 = zeros(mm,mm,pp,smpl);
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0036 Kstar = zeros(mm,pp,smpl);
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0037 P = zeros(mm,mm,smpl+1);
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0038 P1 = P;
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0039 Pstar = zeros(spstar(1),spstar(2),smpl+1); Pstar(:,:,1) = Pstar1;
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0040 Pinf = zeros(spinf(1),spinf(2),smpl+1); Pinf(:,:,1) = Pinf1;
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0041 Pstar1 = Pstar;
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0042 Pinf1 = Pinf;
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0043 crit = options_.kalman_tol;
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0044 crit1 = 1.e-6;
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0045 <a href="steady.html" class="code" title="function steady(linear)">steady</a> = smpl;
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0046 rr = size(Q,1);
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0047 QQ = R*Q*transpose(R);
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0048 QRt = Q*transpose(R);
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0049 alphahat = zeros(mm,smpl);
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0050 etahat = zeros(rr,smpl);
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0051 r = zeros(mm,smpl);
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0052
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0053 Z = zeros(pp,mm);
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0054 <span class="keyword">for</span> i=1:pp;
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0055 Z(i,mf(i)) = 1;
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0056 <span class="keyword">end</span>
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0057
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0058 t = 0;
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0059 icc=0;
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0060 newRank = rank(Pinf(:,:,1),crit1);
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0061 <span class="keyword">while</span> newRank & t < smpl
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0062 t = t+1;
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0063 a1(:,t) = a(:,t);
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0064 Pstar(:,:,t)=tril(Pstar(:,:,t))+transpose(tril(Pstar(:,:,t),-1));
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0065 Pinf(:,:,t)=tril(Pinf(:,:,t))+transpose(tril(Pinf(:,:,t),-1));
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0066 Pstar1(:,:,t) = Pstar(:,:,t);
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0067 Pinf1(:,:,t) = Pinf(:,:,t);
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0068 <span class="keyword">for</span> i=1:pp
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0069 v(i,t) = Y(i,t)-a(mf(i),t)-trend(i,t);
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0070 Fstar(i,t) = Pstar(mf(i),mf(i),t);
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0071 Finf(i,t) = Pinf(mf(i),mf(i),t);
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0072 Kstar(:,i,t) = Pstar(:,mf(i),t);
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0073 <span class="keyword">if</span> Finf(i,t) > crit & newRank, <span class="comment">% original MJ: if Finf(i,t) > crit</span>
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0074 icc=icc+1;
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0075 Kinf(:,i,t) = Pinf(:,mf(i),t);
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0076 Linf(:,:,i,t) = eye(mm) - Kinf(:,i,t)*Z(i,:)/Finf(i,t);
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0077 L0(:,:,i,t) = (Kinf(:,i,t)*Fstar(i,t)/Finf(i,t) - Kstar(:,i,t))*Z(i,:)/Finf(i,t);
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0078 a(:,t) = a(:,t) + Kinf(:,i,t)*v(i,t)/Finf(i,t);
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0079 Pstar(:,:,t) = Pstar(:,:,t) + <span class="keyword">...</span>
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0080 Kinf(:,i,t)*transpose(Kinf(:,i,t))*Fstar(i,t)/(Finf(i,t)*Finf(i,t)) - <span class="keyword">...</span>
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0081 (Kstar(:,i,t)*transpose(Kinf(:,i,t)) +<span class="keyword">...</span>
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0082 Kinf(:,i,t)*transpose(Kstar(:,i,t)))/Finf(i,t);
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0083 Pinf(:,:,t) = Pinf(:,:,t) - Kinf(:,i,t)*transpose(Kinf(:,i,t))/Finf(i,t);
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0084 Pstar(:,:,t)=tril(Pstar(:,:,t))+transpose(tril(Pstar(:,:,t),-1));
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0085 Pinf(:,:,t)=tril(Pinf(:,:,t))+transpose(tril(Pinf(:,:,t),-1));
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0086 <span class="comment">% new terminiation criteria by M. Ratto</span>
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0087 P0=Pinf(:,:,t);
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0088 <span class="comment">% newRank = any(diag(P0(mf,mf))>crit);</span>
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0089 <span class="comment">% if newRank==0, id = i; end,</span>
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0090 <span class="keyword">if</span> ~isempty(options_.diffuse_d),
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0091 newRank = (icc<options_.diffuse_d);
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0092 <span class="comment">%if newRank & any(diag(P0(mf,mf))>crit)==0;</span>
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0093 <span class="keyword">if</span> newRank & (any(diag(P0(mf,mf))>crit)==0 & rank(P0,crit1)==0);
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0094 disp(<span class="string">'WARNING!! Change in OPTIONS_.DIFFUSE_D in univariate DKF'</span>)
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0095 options_.diffuse_d = icc;
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0096 newRank=0;
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0097 <span class="keyword">end</span>
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0098 <span class="keyword">else</span>
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0099 <span class="comment">%newRank = any(diag(P0(mf,mf))>crit);</span>
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0100 newRank = (any(diag(P0(mf,mf))>crit) | rank(P0,crit1));
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0101 <span class="keyword">if</span> newRank==0,
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0102 options_.diffuse_d = icc;
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0103 <span class="keyword">end</span>
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0104 <span class="keyword">end</span>,
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0105 <span class="comment">% if newRank==0,</span>
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0106 <span class="comment">% options_.diffuse_d=i; %this is buggy</span>
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0107 <span class="comment">% end</span>
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0108 <span class="comment">% end new terminiation criteria by M. Ratto</span>
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0109 <span class="keyword">else</span>
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0110 <span class="comment">%% Note that : (1) rank(Pinf)=0 implies that Finf = 0, (2) outside this loop (when for some i and t the condition</span>
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0111 <span class="comment">%% rank(Pinf)=0 is satisfied we have P = Pstar and F = Fstar and (3) Finf = 0 does not imply that</span>
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0112 <span class="comment">%% rank(Pinf)=0. [stphane,11-03-2004].</span>
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0113 Li(:,:,i,t) = eye(mm)-Kstar(:,i,t)*Z(i,:)/Fstar(i,t); <span class="comment">% we need to store Li for DKF smoother</span>
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0114 a(:,t) = a(:,t) + Kstar(:,i,t)*v(i,t)/Fstar(i,t);
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0115 Pstar(:,:,t) = Pstar(:,:,t) - Kstar(:,i,t)*transpose(Kstar(:,i,t))/Fstar(i,t);
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0116 Pstar(:,:,t)=tril(Pstar(:,:,t))+transpose(tril(Pstar(:,:,t),-1));
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0117 <span class="keyword">end</span>
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0118 <span class="keyword">end</span>
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0119 a(:,t+1) = T*a(:,t);
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0120 <span class="keyword">for</span> jnk=1:nk,
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0121 aK(jnk,:,t+jnk) = T^jnk*a(:,t);
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0122 <span class="keyword">end</span>
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0123 Pstar(:,:,t+1) = T*Pstar(:,:,t)*transpose(T)+ QQ;
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0124 Pinf(:,:,t+1) = T*Pinf(:,:,t)*transpose(T);
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0125 P0=Pinf(:,:,t+1);
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0126 <span class="keyword">if</span> newRank,
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0127 <span class="comment">%newRank = any(diag(P0(mf,mf))>crit);</span>
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0128 newRank = rank(P0,crit1);
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0129 <span class="keyword">end</span>
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0130 <span class="keyword">end</span>
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0131
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0132
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0133 d = t;
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0134 P(:,:,d+1) = Pstar(:,:,d+1);
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0135 Linf = Linf(:,:,:,1:d);
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0136 L0 = L0(:,:,:,1:d);
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0137 Fstar = Fstar(:,1:d);
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0138 Finf = Finf(:,1:d);
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0139 Kstar = Kstar(:,:,1:d);
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0140 Pstar = Pstar(:,:,1:d);
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0141 Pinf = Pinf(:,:,1:d);
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0142 Pstar1 = Pstar1(:,:,1:d);
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0143 Pinf1 = Pinf1(:,:,1:d);
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0144 notsteady = 1;
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0145 <span class="keyword">while</span> notsteady & t<smpl
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0146 t = t+1;
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0147 a1(:,t) = a(:,t);
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0148 P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
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0149 P1(:,:,t) = P(:,:,t);
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0150 <span class="keyword">for</span> i=1:pp
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0151 v(i,t) = Y(i,t) - a(mf(i),t) - trend(i,t);
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0152 Fi(i,t) = P(mf(i),mf(i),t);
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0153 Ki(:,i,t) = P(:,mf(i),t);
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0154 <span class="keyword">if</span> Fi(i,t) > crit
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0155 Li(:,:,i,t) = eye(mm)-Ki(:,i,t)*Z(i,:)/Fi(i,t);
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0156 a(:,t) = a(:,t) + Ki(:,i,t)*v(i,t)/Fi(i,t);
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0157 P(:,:,t) = P(:,:,t) - Ki(:,i,t)*transpose(Ki(:,i,t))/Fi(i,t);
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0158 P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
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0159 <span class="keyword">end</span>
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0160 <span class="keyword">end</span>
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0161 a(:,t+1) = T*a(:,t);
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0162 <span class="keyword">for</span> jnk=1:nk,
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0163 aK(jnk,:,t+jnk) = T^jnk*a(:,t);
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0164 <span class="keyword">end</span>
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0165 P(:,:,t+1) = T*P(:,:,t)*transpose(T) + QQ;
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0166 notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<crit);
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0167 <span class="keyword">end</span>
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0168 P_s=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
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0169 Fi_s = Fi(:,t);
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0170 Ki_s = Ki(:,:,t);
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0171 L_s =Li(:,:,:,t);
|
|||
|
|
0172 <span class="keyword">if</span> t<smpl
|
|||
|
|
0173 t_steady = t+1;
|
|||
|
|
0174 P = cat(3,P(:,:,1:t),repmat(P(:,:,t),[1 1 smpl-t_steady+1]));
|
|||
|
|
0175 Fi = cat(2,Fi(:,1:t),repmat(Fi_s,[1 1 smpl-t_steady+1]));
|
|||
|
|
0176 Li = cat(4,Li(:,:,:,1:t),repmat(L_s,[1 1 smpl-t_steady+1]));
|
|||
|
|
0177 Ki = cat(3,Ki(:,:,1:t),repmat(Ki_s,[1 1 smpl-t_steady+1]));
|
|||
|
|
0178 <span class="keyword">end</span>
|
|||
|
|
0179 <span class="keyword">while</span> t<smpl
|
|||
|
|
0180 t=t+1;
|
|||
|
|
0181 a1(:,t) = a(:,t);
|
|||
|
|
0182 <span class="keyword">for</span> i=1:pp
|
|||
|
|
0183 v(i,t) = Y(i,t) - a(mf(i),t) - trend(i,t);
|
|||
|
|
0184 <span class="keyword">if</span> Fi_s(i) > crit
|
|||
|
|
0185 a(:,t) = a(:,t) + Ki_s(:,i)*v(i,t)/Fi_s(i);
|
|||
|
|
0186 <span class="keyword">end</span>
|
|||
|
|
0187 <span class="keyword">end</span>
|
|||
|
|
0188 a(:,t+1) = T*a(:,t);
|
|||
|
|
0189 <span class="keyword">for</span> jnk=1:nk,
|
|||
|
|
0190 aK(jnk,:,t+jnk) = T^jnk*a(:,t);
|
|||
|
|
0191 <span class="keyword">end</span>
|
|||
|
|
0192 <span class="keyword">end</span>
|
|||
|
|
0193 a1(:,t+1) = a(:,t+1);
|
|||
|
|
0194 ri=r;
|
|||
|
|
0195 t = smpl+1;
|
|||
|
|
0196 <span class="keyword">while</span> t>d+1 & t>2,
|
|||
|
|
0197 t = t-1;
|
|||
|
|
0198 <span class="keyword">for</span> i=pp:-1:1
|
|||
|
|
0199 <span class="keyword">if</span> Fi(i,t) > crit
|
|||
|
|
0200 ri(:,t)=transpose(Z(i,:))/Fi(i,t)*v(i,t)+transpose(Li(:,:,i,t))*ri(:,t);
|
|||
|
|
0201 <span class="keyword">end</span>
|
|||
|
|
0202 <span class="keyword">end</span>
|
|||
|
|
0203 r(:,t-1) = ri(:,t);
|
|||
|
|
0204 alphahat(:,t) = a1(:,t) + P1(:,:,t)*r(:,t-1);
|
|||
|
|
0205 etahat(:,t) = QRt*r(:,t);
|
|||
|
|
0206 ri(:,t-1) = transpose(T)*ri(:,t);
|
|||
|
|
0207 <span class="keyword">end</span>
|
|||
|
|
0208 <span class="keyword">if</span> d
|
|||
|
|
0209 r0 = zeros(mm,d); r0(:,d) = ri(:,d);
|
|||
|
|
0210 r1 = zeros(mm,d);
|
|||
|
|
0211 <span class="keyword">for</span> t = d:-1:2
|
|||
|
|
0212 <span class="keyword">for</span> i=pp:-1:1
|
|||
|
|
0213 <span class="keyword">if</span> Finf(i,t) > crit & ~(t==d & i>options_.diffuse_d), <span class="comment">% use of options_.diffuse_d to be sure of DKF termination</span>
|
|||
|
|
0214 <span class="comment">%r1(:,t) = transpose(Z)*v(:,t)/Finf(i,t) + ... BUG HERE in transpose(Z)</span>
|
|||
|
|
0215 r1(:,t) = transpose(Z(i,:))*v(i,t)/Finf(i,t) + <span class="keyword">...</span>
|
|||
|
|
0216 transpose(L0(:,:,i,t))*r0(:,t) + transpose(Linf(:,:,i,t))*r1(:,t);
|
|||
|
|
0217 r0(:,t) = transpose(Linf(:,:,i,t))*r0(:,t);
|
|||
|
|
0218 <span class="keyword">elseif</span> Fstar(i,t) > crit <span class="comment">% step needed whe Finf == 0</span>
|
|||
|
|
0219 r0(:,t)=transpose(Z(i,:))/Fstar(i,t)*v(i,t)+Li(:,:,i,t)'*r0(:,t);
|
|||
|
|
0220 <span class="keyword">end</span>
|
|||
|
|
0221 <span class="keyword">end</span>
|
|||
|
|
0222 alphahat(:,t) = a1(:,t) + Pstar1(:,:,t)*r0(:,t) + Pinf1(:,:,t)*r1(:,t);
|
|||
|
|
0223 r(:,t-1) = r0(:,t);
|
|||
|
|
0224 etahat(:,t) = QRt*r(:,t);
|
|||
|
|
0225 r0(:,t-1) = transpose(T)*r0(:,t);
|
|||
|
|
0226 r1(:,t-1) = transpose(T)*r1(:,t);
|
|||
|
|
0227 <span class="keyword">end</span>
|
|||
|
|
0228 r0_0 = r0(:,1);
|
|||
|
|
0229 r1_0 = r1(:,1);
|
|||
|
|
0230 <span class="keyword">for</span> i=pp:-1:1
|
|||
|
|
0231 <span class="keyword">if</span> Finf(i,1) > crit,
|
|||
|
|
0232 <span class="comment">%r1_0 = transpose(Z)*v(:,1)/Finf(i,1) + ... %bug with Z here</span>
|
|||
|
|
0233 r1_0 = transpose(Z(i,:))*v(i,1)/Finf(i,1) + <span class="keyword">...</span>
|
|||
|
|
0234 transpose(L0(:,:,i,1))*r0_0 + transpose(Linf(:,:,i,1))*r1_0;
|
|||
|
|
0235 r0_0 = transpose(Linf(:,:,i,1))*r0_0;
|
|||
|
|
0236 <span class="keyword">elseif</span> Fstar(i,1) > crit, <span class="comment">% step needed when Finf=0</span>
|
|||
|
|
0237 r0_0=transpose(Z(i,:))/Fstar(i,1)*v(i,1)+Li(:,:,i,1)'*r0_0;
|
|||
|
|
0238 <span class="keyword">end</span>
|
|||
|
|
0239 <span class="keyword">end</span>
|
|||
|
|
0240 <span class="comment">%alphahat(:,1) = a(:,1) + Pstar(:,:,1)*r0_0 + Pinf(:,:,1)*r1_0; %this line is buggy</span>
|
|||
|
|
0241 alphahat(:,1) = a1(:,1) + Pstar1(:,:,1)*r0_0 + Pinf1(:,:,1)*r1_0;
|
|||
|
|
0242 etahat(:,1) = QRt*r(:,1);
|
|||
|
|
0243 <span class="keyword">else</span>
|
|||
|
|
0244 r0 = ri(:,1);
|
|||
|
|
0245 <span class="keyword">for</span> i=pp:-1:1
|
|||
|
|
0246 <span class="keyword">if</span> Fi(i,1) > crit
|
|||
|
|
0247 r0=transpose(Z(i,:))/Fi(i,1)*v(i,1)+transpose(Li(:,:,i,1))*r0;
|
|||
|
|
0248 <span class="keyword">end</span>
|
|||
|
|
0249 <span class="keyword">end</span>
|
|||
|
|
0250 <span class="comment">%alphahat(:,1) = a(:,1) + P(:,:,1)*r0; % this line is buggy</span>
|
|||
|
|
0251 alphahat(:,1) = a1(:,1) + P1(:,:,1)*r0;
|
|||
|
|
0252 etahat(:,1) = QRt*r(:,1);
|
|||
|
|
0253 <span class="keyword">end</span>
|
|||
|
|
0254
|
|||
|
|
0255 a=a(:,1:end-1);</pre></div>
|
|||
|
|
<hr><address>Generated on Fri 16-Jun-2006 09:09:06 by <strong><a href="http://www.artefact.tk/software/matlab/m2html/">m2html</a></strong> © 2003</address>
|
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