covcorr.zip_T matrix_random_收缩估计

function [sigma,shrinkage]=covMarket(x,shrink) % function sigma=covmarket(x) % x (t*n): t iid observations on n random variables % sigma (n*n): invertible covariance matrix estimator % % This estimator is a weighted average of the sample % covariance matrix and a "prior" or "shrinkage target". % Here, the prior is given by a one-factor model. % The factor is equal to the cross-sectional average % of all the random variables. % The notation follows Ledoit and Wolf (2003) % This version: 04/2014 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This file is released under the BSD 2-clause license. % Copyright (c) 2014, Olivier Ledoit and Michael Wolf % All rights reserved. % % Redistribution and use in source and binary forms, with or without % modification, are permitted provided that the following conditions are % met: % % 1. Redistributions of source code must retain the above copyright notice, % this list of conditions and the following disclaimer. % % 2. Redistributions in binary form must reproduce the above copyright % notice, this list of conditions and the following disclaimer in the % documentation and/or other materials provided with the distribution. % % THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS % IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, % THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR % PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR % CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, % EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, % PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR % PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF % LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING % NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS % SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % de-mean returns t=size(x,1); n=size(x,2); meanx=mean(x); x=x-meanx(ones(t,1),:); xmkt=mean(x')'; sample=cov([x xmkt])*(t-1)/t; covmkt=sample(1:n,n+1); varmkt=sample(n+1,n+1); sample(:,n+1)=[]; sample(n+1,:)=[]; prior=covmkt*covmkt'./varmkt; prior(logical(eye(n)))=diag(sample); if (nargin < 2 | shrink == -1) % compute shrinkage parameters c=norm(sample-prior,'fro')^2; y=x.^2; p=1/t*sum(sum(y'*y))-sum(sum(sample.^2)); % r is divided into diagonal % and off-diagonal terms, and the off-diagonal term % is itself divided into smaller terms rdiag=1/t*sum(sum(y.^2))-sum(diag(sample).^2); z=x.*xmkt(:,ones(1,n)); v1=1/t*y'*z-covmkt(:,ones(1,n)).*sample; roff1=sum(sum(v1.*covmkt(:,ones(1,n))'))/varmkt... -sum(diag(v1).*covmkt)/varmkt; v3=1/t*z'*z-varmkt*sample; roff3=sum(sum(v3.*(covmkt*covmkt')))/varmkt^2 ... -sum(diag(v3).*covmkt.^2)/varmkt^2; roff=2*roff1-roff3; r=rdiag+roff; % compute shrinkage constant k=(p-r)/c; shrinkage=max(0,min(1,k/t)) else % use specified number shrinkage = shrink; end % compute the estimator sigma=shrinkage*prior+(1-shrinkage)*sample; shrinkage