我正在尝试使用Kevin Shepperd的工具箱在MATLAB中模拟多元GARCH数据。
他提供的代码文档非常简短，所以我想知道是否有人对此有所了解。
这里是文档。
function [data, Ht] = bekk_simulate(T,k,parameters,p,o,q,type)
% Simulation of symmetric and asymmetric BEKK(p,o,q) multivariate volatility models
%
% USAGE:
% [DATA,HT] = bekk_simulate(T,K,PARAMETERS,P,O,Q,TYPE)
%
% INPUTS:
% T - Either a scalar containing the length of the series to simulate, or a T by K matrix
% of simulated random variables. The default is to use standard normals. Providing
% a T by K matrix allows other distributions to be used.
% PARAMETERS - Vector of parameters. The form of the parameters depends on the TYPE.
% 'Scalar':
% [CC' a(1) ... a(p) g(1) ... g(o) b(1) ... b(q)]' (all scalars)
% 'Diagonal'
% [CC' diag(A(:,:,1))' ... diag(A(:,:,p))' diag(G(:,:,1))' ... diag(G(:,:,o))' diag(B(:,:,1))' ... diag(B(:,:,p))']'
% 'Full'
% [CC' f(A(:,:,1)) ... f(A(:,:,p)) f(G(:,:,1)) ... f(G(:,:,o)) f(B(:,:,1)) ... f(B(:,:,q))]'
% where CC = chol2vec(C')' and f(M) = M(:)'
% P - Positive, scalar integer representing the number of symmetric innovations
% O - Non-negative, scalar integer representing the number of asymmetric innovations
% Q - Non-negative, scalar integer representing the number of conditional covariance lags
% TYPE - String, one of :
% 'Scalar' (Default)
% 'Diagonal'
% 'Full'
%
% OUTPUTS:
% DATA - A T by K matrix of simulated data
% HT - A [K K T] dimension matrix of conditional covariances
%
% COMMENTS:
% The dynamics of a BEKK are given by
%
% H(:,:,t) = C*C' +
% A(:,:,1)'*OP(:,:,t-1)*A(:,:,1) + ... + A(:,:,p)'*OP(:,:,t-1)*A(:,:,p) +
% G(:,:,1)'*OPA(:,:,t-1)*G(:,:,1) + ... + G(:,:,o)'*OPA(:,:,t-1)*G(:,:,o) +
% B(:,:,1)'*G(:,:,t-1)*B(:,:,1) + ... + B(:,:,q)'*OP(:,:,t-1)*B(:,:,q)
%
% where in the scalar model A(:,:,i) = a(i)*eye(K) (similarly for G and B).
%
% EXAMPLES:
% % Scalar with A.^2=.05, G.^2=.1 and B.^2=.88
% CCp = [1 .5;.5 4];
% parameters = [chol2vec(chol(CCp)');sqrt([.05,.10,.88])']
% [data,Ht] = bekk_simulate(1000,2,parameters,1,1,1,'Scalar')
% % Diagonal
% parameters = [chol2vec(chol(CCp)');sqrt([.05 .07 .93 .88])']
% [data,Ht] = bekk_simulate(1000,2,parameters,1,0,1,'Diagonal')
%
% See also BEKK
可以说我估计了一个GARCH模型，我已经在RATS中完成了这个工作，并且我想根据该规范生成一些数据，我该如何使用上面的函数来做到这一点：
5. C(1,1) 0.997031034 0.508107063 1.96225 0.04973386
6. C(2,1) 1.733801614 0.123673427 14.01919 0.00000000
7. C(2,2) -1.176292837 0.086098995 -13.66210 0.00000000
8. A(1,1) 0.298475449 0.046993702 6.35139 0.00000000
9. A(1,2) -0.124095879 0.070112013 -1.76997 0.07673281
10. A(2,1) 0.061551419 0.031864938 1.93163 0.05340461
11. A(2,2) 0.355969936 0.039672897 8.97262 0.00000000
12. B(1,1) 1.147042406 0.035509033 32.30283 0.00000000
13. B(1,2) 0.741209244 0.037170906 19.94058 0.00000000
从文档中，我会猜到我已经装满了，我可以使用以下输入来简单地模拟数据：
C = [0.997 1.734 -1.176];
A = [0.298 -0.124 0.062 0.356];
B = [1.147 0.741 -0.400 0.468];
parameters =[C A(:)' B(:)' ]'; %this is for the BEKK(1,1)
[errors, Ht] = bekk_simulate(nobs,k,parameters,1,0,1,'Full');
然后，我显然会填写该函数运行所需的缺少的内容。
一位同事问一个问题，我是否需要先对参数求平方根？