Python scipy.minimize : overflow encountered in double_scalars and invalid value encountered in double_scalars

Question

我构建了一个自定义的 EST(指数平滑)模型。首先，我定义了一个函数，其中包含传递给第二个函数的参数定义，该函数执行计算并返回预测错误。然后将这些平方并求和。然后，最小化器应优化参数，以便最小化平方误差的总和。
如果我让函数以起始值运行，则该模型有效。但是一旦我把它从 scipy 中抛出最小化，它就会多次给我以下两个错误:
RuntimeWarning: double_scalars 中遇到溢出
运行时警告:在 double_scalars 中遇到无效值
我检查了我的数据 (y) 并且没有零值。因此计算不应返回任何零。
此外，我尝试了边界和其他最小化方法，这也无济于事。
(这些是我从其他问题中得到的想法)
任何帮助是极大的赞赏 :)
'''

from scipy.optimize import minimize

def model(params, y):

    alpha = params[0] 
    beta = params[1]
    gamma = params[2]
    omega = params[3]
    l_init_HM = params[4]
    b_init_HM = params[5]
    s_init7_HM = params[6]
    s_init6_HM = params[7]
    s_init5_HM = params[8]
    s_init4_HM = params[9]
    s_init3_HM = params[10]
    s_init2_HM = params[11]
    s_init_HM = params[12]
    
    results = ETS_M_Ad_M(alpha,beta,gamma,omega,
          l_init_HM,b_init_HM,s_init7_HM,
          s_init6_HM,s_init5_HM,s_init4_HM,
         s_init3_HM,s_init2_HM,s_init_HM,y)
    
    error_list = results['errors_list']
    
    error_list = [number ** 2 for number in error_list]
    
    #returning the sum of squared errors
    #this is the ML estimate, or rather Adjusted Least Squared (ALS)
    #Hyndman p. 69
    error_sum = sum(error_list)
   
    return error_sum

def ETS_M_Ad_M(alpha,beta,gamma,omega,
              l_init_HM,b_init_HM,s_init7_HM, 
              s_init6_HM,s_init5_HM,s_init4_HM,
             s_init3_HM,s_init2_HM,s_init_HM,y):
        
        #computing the number of time points as the length of the forecasting vector
        t = len(y)
        errors_list = list()
        point_forecast = list()
        l_list = list()
        b_list = list()
        s_list = list()
        
        #parameter definition
    
        #Initilaisation
        l_past = l_init_HM
        b_past = b_init_HM
        s_past = s_init7_HM
        s_past7 = s_init6_HM
        s_past6 = s_init5_HM
        s_past5 = s_init4_HM
        s_past4 = s_init3_HM
        s_past3 = s_init2_HM
        s_past2 = s_init_HM
    
        mu = (l_past + omega * b_past) * s_past
        #compute forecasting error at timepoint t
        e = (y[0] - mu) / y[0]
        #compute absolute errors for ML estimation
        e_absolute = y[0] - mu
    
        #save estimation error for Likelihood computation
        errors_list.append(e_absolute)
        point_forecast.append(mu)
        l_list.append(l_past)
        b_list.append(b_past)
        s_list.append(s_past)
    
        #Updating
        #updating all state estimates for time point t
        l = (l_past + omega * b_past) * (1 + alpha * e)
        b = omega * b_past + beta * (l_past + omega * b_past) * e
        s = s_past * (1 + gamma * e)
    
    
        #computation loop:
        for i in range(1,t): #start at 1 as the first index '0' is used in the initialization
            #Prediciton
            #denote updated states from t-1 as past states for time point t
            l_past = l
            b_past = b
            s_past7 = s_past6
            s_past6 = s_past5
            s_past5 = s_past4
            s_past4 = s_past3
            s_past3 = s_past2
            s_past2 =  s
    
            #Observation
            #compute one step ahead  forecast for timepoint t
            mu = (l_past + omega * b_past) * s_past
            #compute forecasting error at timepoint t
            e = (y[i] - mu) / y[i]
            #compute absolute errors for ML estimation
            e_absolute = y[i] - mu
    
            #save estimation error for Likelihood computation
            #saving squared errors
            errors_list.append(e_absolute) 
            point_forecast.append(mu)
            l_list.append(l_past)
            b_list.append(b_past)
            s_list.append(s_past)
    
            #Updating
            #updating all state estimates for time point t
            l = (l_past + omega * b_past) * (1 + alpha * e)
            b = omega * b_past + beta * (l_past + omega * b_past) * e
            s = s_past * (1 + gamma * e)
    
        return  {'errors_list' : errors_list, 'point forecast' : point_forecast,
                 'l_list' : l_list, 'b_list' : b_list, 's_list' : s_list}

#Defining Starting Parameters
Starting_Parameters = [0.1, #alpha
                       0.01, #beta
                       0.01, #Gamma
                       0.99, #omega 
                       5556.151751807499, #l_init
                       92.90080519198762, #b_init
                       1.256185460504065, #s_init7
                       1.0317387565497154, #s_init6
                       0.8373829313978448, #s_init5
                       0.8220047728017161, #s_init4
                       0.8461049900287951, #s_init3
                       0.9412435736696254, #s_init2
                       1.2653395150482378] #s_init
# -> starting values from Hyndman 2008 p.24


    minimize(model, Starting_Parameters, args=(y), method='BFGS')

'''

y 中包含的时间序列通过以下链接上传到我的 GitHub:
https://github.com/MatthiasHerp/Public/blob/master/revenue_CA_1_FOODS_day.csv
只需导入它并将其存储为 y，代码就应该运行 :)

Answer 1

alpha、beta、gamma 和 omega 不应该限制在 0 和 1 之间吗？
此外您忘记分配 s_past在 for 循环中。