DM test.rar_-baijiahao_DM 检验_DM-test_DM检验_dmtest检验

function [DM,p_value] = dmtest(e1, e2, h) %DMTEST: Retrieves the Diebold-Mariano test statistic (1995) for the % equality of forecast accuracy of two forecasts under general assumptions. % % DM = dmtest(e1, e2, ...) calculates the D-M test statistic on the base % of the loss differential which is defined as the difference of the % squared forecast errors % % In particular, with the DM statistic one can test the null hypothesis: % H0: E(d) = 0. The Diebold-Mariano test assumes that the loss % differential process 'd' is stationary and defines the statistic as: % DM = mean(d) / sqrt[ (1/T) * VAR(d) ] ~ N(0,1), % where VAR(d) is an estimate of the unconditional variance of 'd'. % % This function also corrects for the autocorrelation that multi-period % forecast errors usually exhibit. Note that an efficient h-period % forecast will have forecast errors following MA(h-1) processes. % Diebold-Mariano use a Newey-West type estimator for sample variance of % the loss differential to account for this concern. % % 'e1' is a 'T1-by-1' vector of the forecast errors from the first model % 'e2' is a 'T2-by-1' vector of the forecast errors from the second model % % It should hold that T1 = T2 = T. % % DM = DMTEST(e1, e2, 'h') allows you to specify an additional parameter % value 'h' to account for the autocorrelation in the loss differential % for multi-period ahead forecasts. % 'h' the forecast horizon, initially set equal to 1 % % DM = DMTEST(...) returns a constant: % 'DM' the Diebold-Mariano (1995) test statistic % % Semin Ibisevic (2011) % $Date: 11/29/2011 $ % % ------------------------------------------------------------------------- % References % K. Bouman. Quantitative methods in international finance and % macroeconomics. Econometric Institute, 2011. Lecture FEM21004-11. % % Diebold, F.X. and R.S. Mariano (1995), "Comparing predictive accuracy", % Journal of Business & Economic Statistics, 13, 253-263. % ------------------------------------------------------------------------- if nargin < 2 error('dmtest:TooFewInputs','At least two arguments are required'); end if nargin < 3 h = 1; end if size(e1,1) ~= size(e2,1) || size(e1,2) ~= size(e2,2) error('dmtest:InvalidInput','Vectors should be of equal length'); end if size(e1,2) > 1 || size(e2,2) > 1 error('dmtest:InvalidInput','Input should have T rows and 1 column'); end % Initialization T = size(e1,1); % Define the loss differential d = e1.^2 - e2.^2; % Ralculate the variance of the loss differential, taking into account % autocorrelation. dMean = mean(d); % gamma0 = var(d); % cov(d) or cov(d(1+k:T),d(1:T-k)) k is lag time if h > 1 gamma = zeros(h-1,1); for i = 1:h-1 gamma(i) = (d(1+i:T)' * d(1:T-i)) ./ T; % bugfix end varD = gamma0 + 2*sum(gamma); else varD = gamma0; end % Retrieve the diebold mariano statistic DM ~N(0,1) DM = dMean / sqrt ( (1/T)*varD ); p_value = (1- normcdf(DM) ); % P = erfc(-z/sqrt(2))/2; % Equivalent to ��normcdf�� % Bugfix: taking longer horizons triggers an occurance of a negative % variance estimator when using % sampleCov = cov(d(1+i:T),d(1:T-i)); % gamma(i) = sampleCov(2);