加权灰色马尔科夫模型的代码

加权灰色马尔科夫模型（Weighted Grey Markov Model, WGMM）是一种基于灰色理论和马尔科夫模型的预测方法，常用于处理具有周期性、趋势性和不确定性的时间序列数据。下面是一份用Python实现WGMM的代码示例：

import numpy as np

class WGMM:
    def __init__(self, data, k, w):
        self.data = data
        self.k = k
        self.w = w
        
    def _normalize(self, X): # 数据归一化
        return (X - np.min(X)) / (np.max(X) - np.min(X))
    
    def _calculate_weights(self): # 计算权重
        X = self._normalize(self.data)
        n = len(X)
        weights = np.zeros((n, self.k))
        for i in range(self.k):
            weights[i][0] = X[i]
        for i in range(self.k, n):
            weights[i][0] = X[i]
            for j in range(1, self.k):
                weights[i][j] = np.sum(X[i-j:i]) / np.sum(X[i-j+1:i+1])
        return weights
    
    def _calculate_probabilities(self, weights): # 计算概率矩阵
        n = len(weights)
        probabilities = np.zeros((n-1, self.k, self.k))
        for i in range(1, n):
            for j in range(self.k):
                row_sum = np.sum(weights[i-1])
                if row_sum == 0:
                    continue
                for l in range(self.k):
                    probabilities[i-1][j][l] = (weights[i-1][j] * self.w[l] + weights[i][l]) / row_sum
        return probabilities
    
    def fit(self): # 训练模型
        weights = self._calculate_weights()
        probabilities = self._calculate_probabilities(weights)
        self.weights = weights
        self.probabilities = probabilities
        
    def predict(self, steps=1): # 预测
        n = len(self.data)
        X = self._normalize(self.data)
        y_pred = np.zeros(steps)
        for i in range(n, n+steps):
            if i == n:
                y_pred[i-n] = X[i-1]
            else:
                y_i = np.zeros(self.k)
                for j in range(self.k):
                    y_i[j] = np.sum(X[i-j:i] * self.weights[i-1][j])
                y_pred[i-n] = np.sum([y_i[l] * self.probabilities[i-n-1][j][l] for j in range(self.k) for l in range(self.k)])
        return y_pred

其中，`data`是输入的时间序列数据，`k`是WGMM模型的阶数，`w`是权重向量，表示不同阶数的权重。`fit()`方法用于训练模型，`predict()`方法用于预测未来的时间序列数据。