超出某一限定值的相关性，验证是否存在非对称效应

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qc2 = qc;
    for jj=1:length(qc);
        temp1 = find( (X<=quantile(X,1-qc(jj))).*(Y<=quantile(Y,1-qc(jj))) );
        temp2 = find( (X>=quantile(X,qc(jj))).*(Y>=quantile(Y,qc(jj))) );
        if ((length(temp1)<3)+(length(temp2)<3))>0  % then not enough data to compute a correlation in at least one tail
            qc2 = setdiff(qc2,qc(jj));
        end
    end

    % now I am sure that each cut-off has enough data
    qc2 = sortrows(unique([qc2;1-qc2]));   % sorting and making sure that 0 does not appear twice   
    if isempty(find(qc==0.5))==0    % then q=0.5 is a cut-off
        qc1 = [qc2(1:(end+1)/2);qc2((end+1)/2:end)];
    else
        qc1 = qc2;
    end
    q = qc1(end/2+1:end);

    k = length(q);
    xi = nines(T,k);    % variable used in constructing test statistic
    rhodiff = nines(k,1);
    for jj = 1:k;
        temp1 = find( (X<=quantile(X,1-qc(jj))).*(Y<=quantile(Y,1-qc(jj))) );
        temp2 = find( (X>=quantile(X,qc(jj))).*(Y>=quantile(Y,qc(jj))) );
        out1(jj,1) = corrcoef12(X(temp1),Y(temp1));
        out1(end+1-jj,1) = corrcoef12(X(temp2),Y(temp2));
        rhodiff(jj) = corrcoef12(X(temp2),Y(temp2)) - corrcoef12(X(temp1),Y(temp1));      % computing the test stat

        x1plus = (X-mean(X(temp2)))./std(X(temp2));
        x2plus = (Y-mean(Y(temp2)))./std(Y(temp2));
        x1minus = (X-mean(X(temp1)))./std(X(temp1));
        x2minus = (Y-mean(Y(temp1)))./std(Y(temp1));

        xi(:,jj) = T/size(temp2,1)*(x1plus.*x2plus - corrcoef12(X(temp2),Y(temp2))).*( (X>=quantile(X,qc(jj))).*(Y>=quantile(Y,qc(jj))) ) - ...
            T/size(temp1,1)*(x1minus.*x2minus - corrcoef12(X(temp1),Y(temp1))).*( (X<=quantile(X,1-qc(jj))).*(Y<=quantile(Y,1-qc(jj))) );
    end
    omegahat = newey_west(xi);      % computing the covariance matrix
    teststat = T*rhodiff'*inv(omegahat)*rhodiff;
    pval = 1-chi2cdf(teststat,k);

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关键词：相关性 quantile corrcoef length quant