ARIMA-GM(1,1)-BP模型代码

由于ARIMA-GM(1,1)-BP模型结合了三个模型，代码可能较为复杂，下面提供一个基本的代码框架供参考：

# 导入相关库
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.tsa.arima.model import ARIMA
from sklearn.neural_network import MLPRegressor
from sklearn.preprocessing import MinMaxScaler

# 读取数据
data = pd.read_csv('data.csv', index_col=0, parse_dates=True)
train_data = data['2010':'2018']
test_data = data['2019':'2020']

# ARIMA模型训练
model = ARIMA(train_data, order=(1,1,1))
model_fit = model.fit()
residuals = pd.DataFrame(model_fit.resid)

# GM(1,1)模型预测
def gm11(x0):
    x1 = np.cumsum(x0)
    z1 = (x1[:-1] + x1[1:]) / 2.0
    z1 = z1.reshape((len(z1), 1))
    B = np.append(-z1, np.ones_like(z1), axis=1)
    Y = x0[1:].reshape((len(x0) - 1, 1))
    [[a], [b]] = np.dot(np.dot(np.linalg.inv(np.dot(B.T, B)), B.T), Y)
    result = (x0[0] - b / a) * np.exp(-a * np.arange(len(x0)))
    return result

x0 = train_data['y'].values
y0 = gm11(x0)

# BP神经网络模型训练
scaler = MinMaxScaler(feature_range=(0, 1))
X_train = scaler.fit_transform(y0.reshape(-1, 1))
y_train = scaler.fit_transform(train_data['y'].values.reshape(-1, 1))
model = MLPRegressor(hidden_layer_sizes=(10, 10), activation='relu', solver='adam', max_iter=1000)
model.fit(X_train, y_train)

# 预测
x1 = test_data['y'].values
y1 = gm11(x1)
X_test = scaler.transform(y1.reshape(-1, 1))
y_pred = model.predict(X_test)
y_pred = scaler.inverse_transform(y_pred)

# 可视化
plt.plot(test_data.index, y_pred, label='Predicted')
plt.plot(test_data.index, test_data['y'].values, label='Actual')
plt.legend()
plt.show()

需要注意的是，上述代码中的数据读取方式、GM(1,1)模型的实现方式、BP神经网络模型的参数设置等均需要根据具体情况进行修改。