将MATLAB的fminsearch及其约束转换为scipy的minimize

Question

我想最大化GARCH模型的对数似然函数，我在MATLAB中使用fminsearch来最小化负对数似然函数，此问题有两个约束。我尝试使用fmin或minimize函数（来自scipy），但我认为转换约束的方法不正确。

以下是我在python 3.6中的尝试：

def computeNegLLH(parameters):
    sigma2 =  np.zeros(len(returns));

    omega = parameters[0];
    alpha = parameters[1];
    beta  = parameters[2];
    sigma2[1] = parameters[3];

    # parameters restrictions: omega>0; alpha,beta>=0; alpha + beta >= 1
    if (omega<=0 or min(alpha,beta)<0 or alpha + beta >= 1 or sigma2[0]<=0):
    negLLH = sys.maxsize;
    sys.exit();

    # calculate squared returns
    returns2 = returns**2;


    for t in range(1,len(returns)):
    sigma2[t]= omega + alpha*returns2[t-1] + beta*sigma2[t-1];

   # calculate (-1)xLogLikelihood for a GARCH(1,1) process with parameters
   negLLH = 0.5*sum(log(sigma2) + returns2/sigma2);
   return negLLH


result = minimize(fun = computeNegLLH, x0 = startingValues, method = 'Nelder- 
Mead', options = {'xtol': 1e-8})

我的MATLAB代码：

function param = calibrate_GARCH(returns, startingValues)
    % computes maximum likelhood estimates for a GARCH(1,1) process give
    % timeseries "returns" using fminsearch function 
    options = optimset('TolX',1e-12,'MaxFunEvals',3000,'Maxiter',3000, 
    'Display','off','LargeScale','off');
    param = fminsearch(@(param)computeNegLLH(param,returns), startingValues, 
    options);
end

function negLLH = computeNegLLH(param,returns)
    % param for the given timeseries returns
    sigma2 =  zeros(size(returns));

    omega = param(1);
    alpha = param(2);
    beta  = param(3);
    sigma2(1) = param(4);

    % parameter restrictions: omega>0 alpha,beta>=0
    % ensure that GARCH(1,1) process is covariance-stationary
    if omega<=0 || min(alpha,beta)<0 || alpha + beta >= 1 || sigma2(1)<=0;
        negLLH = intmax;
        return;
    end

    % calculate squared returns
    returns2 = returns.^2;

    for t=2:length(returns)
        sigma2(t)= omega + alpha*returns2(t-1) + beta*sigma2(t-1);
    end
    % computes (-1)xLogLikelihood for a GARCH(1,1) process with parameters
    negLLH = 0.5*sum(log(sigma2) + returns2./sigma2);
end