Python 使用Statsmodels MLEmodel构建自定义状态空间模型

我正在研究如何使用python中的状态空间模型构建状态空间模型的自定义模型。 我想知道是否应该在下面的URL中使用statsomdel的MLEmodel类，但我不确定如何构建它。

具体来说，我想使用以下模型进行长期预测

1.状态方程

x_t=x_{t-1}+A exp（B/z_{t-1}）+E_{1t}

• x_t：时间t的状态
• x{t-1}：时间t-1时的状态
• A：常数（要估计的参数）
• B：常数（要估计的参数）
• z_{t-1}：解释变量
• E_{1t}：系统噪声（~N（0，u_1））

观测方程 y_t=x_t+E_{2t}

• 是：观测数据（传感）
• E_{2t}：观测噪声（~N（0，u_2））

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请告诉我

您的模型的基本实现是（编辑以添加预测所需的方法）：

对不起。富尔顿先生

我想在方程中加一个常数项T，如下所示。 我是否应该更改“转换”的规格说明方法

状态方程： x_t=tx_{t-1}+A exp（B/z_{t-1}）+E_{1t}

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谢谢你，富尔顿先生！我很荣幸能直接收到开发者的来信。没问题，我希望它有用。对不起。富尔顿先生，我想在方程中加一个常数项T，如下所示。我是否应该改变“过渡”的规格说明方法？富尔顿先生。请告诉我。是否可以增加自定义状态空间模型中的滞后数？（t-2，t-3，t-4，t-5，，，，，）@cfulton

import numpy as np
import statsmodels.api as sm

class RWD(sm.tsa.statespace.MLEModel):
    param_names = ['A', 'B', 'u_1', 'u_2']
    start_params = [1., 0., 1., 1]

    def __init__(self, endog, exog):
        exog = np.squeeze(exog)
        super().__init__(endog, exog=exog, k_states=1, initialization='diffuse')
        self.k_exog = 1
        
        # Z = I
        self['design', 0, 0] = 1.
        # T = I
        self['transition', 0, 0] = 1.
        # R = I
        self['selection', 0, 0] = 1.
        
        # Set c_t to be time-varying
        self['state_intercept'] = np.zeros((1, self.nobs))
        
    def clone(self, endog, exog, **kwargs):
        # This method must be set to allow forecasting in custom
        # state space models that include time-varying state
        # space matrices, like we have for state_intercept here
        return self._clone_from_init_kwds(endog, exog=exog, **kwargs)
        
    def transform_params(self, params):
        # Variances must be positive
        params[2:] = params[2:]**2
        return params
        
    def untransform_params(self, params):
        # Reverse of above transformation
        params[2:] = params[2:]**0.5
        return params
    
    def update(self, params, **kwargs):
        params = super().update(params, **kwargs)
        
        # c_t = A * exp(B / z_t)
        self['state_intercept', 0, :] = params[0] * np.exp(params[1] / self.exog)
        
        # H = u_1
        self['obs_cov', 0, 0] = params[2]
        # Q = u_2
        self['state_cov', 0, 0] = params[3]

import numpy as np
import statsmodels.api as sm

class RWD(sm.tsa.statespace.MLEModel):
    param_names = ['T', 'A', 'B', 'u_1', 'u_2']
    start_params = [1., 1., 0., 1., 1]

    def __init__(self, endog, exog):
        exog = np.squeeze(exog)
        super().__init__(endog, exog=exog, k_states=1, initialization='diffuse')
        self.k_exog = 1
        
        # Z = I
        self['design', 0, 0] = 1.
        # T = I
        #self['transition', 0, 0] = 1.
        # R = I
        self['selection', 0, 0] = 1.
        
        # Set c_t to be time-varying
        self['state_intercept'] = np.zeros((1, self.nobs))
        
    def clone(self, endog, exog, **kwargs):
        #This method must be set to allow forecasting in custom
        #state space models that include time-varying state
        #space matrices, like we have for state_intercept here
        return self._clone_from_init_kwds(endog, exog=exog, **kwargs)
        
    def transform_params(self, params):
        # Variances must be positive
        params[3:] = params[3:]**2
        return params
        
    def untransform_params(self, params):
        # Reverse of above transformation
        params[3:] = params[3:]**0.5
        return params
    
    def update(self, params, **kwargs):
        params = super().update(params, **kwargs)
        # T = T
        self['transition', 0, 0] = params[0] 
        # c_t = A * exp(B / z_t)
        self['state_intercept', 0, :] = params[1] * np.exp(params[2] / self.exog)
        
        # H = u_1
        self['obs_cov', 0, 0] = params[3]
        # Q = u_2
        self['state_cov', 0, 0] = params[4]