function var=rfvar3(ydata,lags,xdata,breaks,lambda,mu)
This algorithm goes for accuracy without worrying about memory requirements.
ydata: dependent variable data matrix
xdata: exogenous variable data matrix
lags: number of lags
breaks: rows in ydata and xdata after which there is a break. This allows for
discontinuities in the data (e.g. war years) and for the possibility of
adding dummy observations to implement a prior. This must be a column vector.
Note that a single dummy observation becomes lags+1 rows of the data matrix,
with a break separating it from the rest of the data. The function treats the
first lags observations at the top and after each "break" in ydata and xdata as
initial conditions.
lambda: weight on "co-persistence" prior dummy observations. This expresses
belief that when data on *all* y's are stable at their initial levels, they will
tend to persist at that level. lambda=5 is a reasonable first try. With lambda<0,
constant term is not included in the dummy observation, so that stationary models
with means equal to initial ybar do not fit the prior mean. With lambda>0, the prior
implies that large constants are unlikely if unit roots are present.
mu: weight on "own persistence" prior dummy observation. Expresses belief
that when y_i has been stable at its initial level, it will tend to persist
at that level, regardless of the values of other variables. There is
one of these for each variable. A reasonable first guess is mu=2.
The program assumes that the first lags rows of ydata and xdata are real data, not dummies.
Dummy observations should go at the end, if any. If pre-sample x's are not available,
repeating the initial xdata(lags+1,:) row or copying xdata(lags+1:2*lags,:) into
xdata(1:lags,:) are reasonable subsititutes. These values are used in forming the
persistence priors.
Code written by Christopher Sims. This version 6/15/03.0001 function var=rfvar3(ydata,lags,xdata,breaks,lambda,mu) 0002 %function var=rfvar3(ydata,lags,xdata,breaks,lambda,mu) 0003 % This algorithm goes for accuracy without worrying about memory requirements. 0004 % ydata: dependent variable data matrix 0005 % xdata: exogenous variable data matrix 0006 % lags: number of lags 0007 % breaks: rows in ydata and xdata after which there is a break. This allows for 0008 % discontinuities in the data (e.g. war years) and for the possibility of 0009 % adding dummy observations to implement a prior. This must be a column vector. 0010 % Note that a single dummy observation becomes lags+1 rows of the data matrix, 0011 % with a break separating it from the rest of the data. The function treats the 0012 % first lags observations at the top and after each "break" in ydata and xdata as 0013 % initial conditions. 0014 % lambda: weight on "co-persistence" prior dummy observations. This expresses 0015 % belief that when data on *all* y's are stable at their initial levels, they will 0016 % tend to persist at that level. lambda=5 is a reasonable first try. With lambda<0, 0017 % constant term is not included in the dummy observation, so that stationary models 0018 % with means equal to initial ybar do not fit the prior mean. With lambda>0, the prior 0019 % implies that large constants are unlikely if unit roots are present. 0020 % mu: weight on "own persistence" prior dummy observation. Expresses belief 0021 % that when y_i has been stable at its initial level, it will tend to persist 0022 % at that level, regardless of the values of other variables. There is 0023 % one of these for each variable. A reasonable first guess is mu=2. 0024 % The program assumes that the first lags rows of ydata and xdata are real data, not dummies. 0025 % Dummy observations should go at the end, if any. If pre-sample x's are not available, 0026 % repeating the initial xdata(lags+1,:) row or copying xdata(lags+1:2*lags,:) into 0027 % xdata(1:lags,:) are reasonable subsititutes. These values are used in forming the 0028 % persistence priors. 0029 % Code written by Christopher Sims. This version 6/15/03. 0030 [T,nvar]=size(ydata); 0031 nox=isempty(xdata); 0032 if ~nox 0033 [T2,nx]=size(xdata); 0034 else 0035 T2=T;nx=0;xdata=zeros(T2,0); 0036 end 0037 % note that x must be same length as y, even though first part of x will not be used. 0038 % This is so that the lags parameter can be changed without reshaping the xdata matrix. 0039 if T2 ~= T, disp('Mismatch of x and y data lengths'),end 0040 if nargin<4 0041 nbreaks=0;breaks=[]; 0042 else 0043 nbreaks=length(breaks); 0044 end 0045 breaks=[0;breaks;T]; 0046 smpl=[]; 0047 for nb=1:nbreaks+1 0048 smpl=[smpl;[breaks(nb)+lags+1:breaks(nb+1)]']; 0049 end 0050 Tsmpl=size(smpl,1); 0051 X=zeros(Tsmpl,nvar,lags); 0052 for is=1:length(smpl) 0053 X(is,:,:)=ydata(smpl(is)-(1:lags),:)'; 0054 end 0055 X=[X(:,:) xdata(smpl,:)]; 0056 y=ydata(smpl,:); 0057 % Everything now set up with input data for y=Xb+e 0058 % ------------------Form persistence dummies------------------- 0059 if lambda~=0 | mu>0 0060 ybar=mean(ydata(1:lags,:),1); 0061 if ~nox 0062 xbar=mean(xdata(1:lags,:),1); 0063 else 0064 xbar=[]; 0065 end 0066 if lambda~=0 0067 if lambda>0 0068 xdum=lambda*[repmat(ybar,1,lags) xbar]; 0069 else 0070 lambda=-lambda; 0071 xdum=lambda*[repmat(ybar,1,lags) zeros(size(xbar))]; 0072 end 0073 ydum=zeros(1,nvar); 0074 ydum(1,:)=lambda*ybar; 0075 y=[y;ydum]; 0076 X=[X(:,:);xdum]; 0077 end 0078 if mu>0 0079 xdum=[repmat(diag(ybar),1,lags) zeros(nvar,nx)]*mu; 0080 ydum=mu*diag(ybar); 0081 X=[X;xdum]; 0082 y=[y;ydum]; 0083 end 0084 end 0085 [vl,d,vr]=svd(X(:,:),0); 0086 di=1../diag(d); 0087 B=vl'*y; 0088 B=(vr.*repmat(di',nvar*lags+nx,1))*B; 0089 u=y-X(:,:)*B; 0090 xxi=vr.*repmat(di',nvar*lags+nx,1); 0091 xxi=xxi*xxi'; 0092 B=reshape(B,[nvar*lags+nx,nvar]); % rhs variables, equations 0093 By=B(1:nvar*lags,:); 0094 By=reshape(By,nvar,lags,nvar);% variables, lags, equations 0095 By=permute(By,[3,1,2]); %equations, variables, lags to match impulsdt.m 0096 if nox 0097 Bx=[]; 0098 else 0099 Bx=B(nvar*lags+(1:nx),:)'; 0100 end 0101 %logintlh=matrictint(u'*u,xxi,size(X,1)-nvar-1)-.5*nvar*(nvar+1)*log(2*pi); 0102 var.By=By;var.Bx=Bx;var.u=u;var.xxi=xxi;%var.logintlh=logintlh; 0103 % Desired features: 1) automatic dummies for vcv prior 0104 % 2) automatic calculation of integrated pdf, accounting 0105 % for the dummy variables as a prior 0106 % 3) automatic dummies for "Minnesota prior"