arima-xgboost 代码实现，使用网格搜索与时间序列分割TimeSeriesSplit优化xgboost模型，

首先，我们需要导入需要的库和数据集。假设我们使用的是一个名为 `data` 的 Pandas DataFrame，其中包含时间序列数据。

import pandas as pd
import numpy as np
from sklearn.metrics import mean_squared_error
from sklearn.model_selection import ParameterGrid, TimeSeriesSplit
from statsmodels.tsa.arima_model import ARIMA
import xgboost as xgb

# 导入数据集
data = pd.read_csv('data.csv')

接下来，我们可以将数据集分成训练集和测试集。在这里，我们将使用前80%的数据作为训练集，后20%的数据作为测试集。我们还需要定义时间序列分割的参数，以便用于交叉验证。

# 将数据集分成训练集和测试集
train_size = int(len(data) * 0.8)
train_data, test_data = data[:train_size], data[train_size:]

# 定义时间序列分割参数
n_splits = 5
window_size = int(len(train_data) / n_splits)
tscv = TimeSeriesSplit(n_splits=n_splits)

接下来，我们将使用ARIMA模型对训练数据进行拟合，以便将其用作XGBoost模型的特征。我们使用ARIMA模型的残差作为特征，因为残差包含了时间序列中未被模型捕捉到的信息。我们将使用ARIMA模型的残差和原始数据的移动平均值和标准差作为XGBoost模型的特征。

# 定义ARIMA模型的参数和范围
p = [0, 1, 2]
d = [0, 1]
q = [0, 1, 2]
arima_params = list(ParameterGrid({'p': p, 'd': d, 'q': q}))

# 定义XGBoost模型的参数和范围
xgb_params = {'max_depth': [3, 5, 7], 'n_estimators': [50, 100, 150]}

# 定义特征变量和目标变量
train_features = []
train_targets = []

# 对每个时间序列分割进行ARIMA模型拟合和特征提取
for train_index, test_index in tscv.split(train_data):
    # 定义训练集和测试集
    train, test = train_data.iloc[train_index], train_data.iloc[test_index]

    # 对训练集进行ARIMA模型拟合
    arima_model = ARIMA(train, order=(1, 1, 0))
    arima_fit = arima_model.fit(disp=0)

    # 提取ARIMA模型残差
    arima_residuals = pd.DataFrame(arima_fit.resid)
    arima_residuals.index = train.index[1:]

    # 提取移动平均值和标准差
    rolling_mean = train.rolling(window=window_size).mean()[window_size:]
    rolling_std = train.rolling(window=window_size).std()[window_size:]

    # 将ARIMA模型残差、移动平均值和标准差作为特征
    train_features.append(pd.concat([arima_residuals, rolling_mean, rolling_std], axis=1))
    train_targets.append(train.iloc[1:])

# 将特征和目标变量转换为NumPy数组
train_features = np.concatenate(train_features)
train_targets = np.concatenate(train_targets).ravel()

现在我们可以使用网格搜索来找到最佳的XGBoost模型。我们将使用均方根误差（RMSE）作为评估指标。

# 定义网格搜索参数
grid = ParameterGrid({'xgb_params': xgb_params, 'arima_params': arima_params})

# 定义最佳模型参数和最小RMSE
best_params = None
min_rmse = float('inf')

# 对每个参数组合进行交叉验证
for params in grid:
    # 定义XGBoost模型和ARIMA模型
    xgb_model = xgb.XGBRegressor(**params['xgb_params'])
    arima_model = ARIMA(train_data, order=(params['arima_params']['p'], params['arima_params']['d'], params['arima_params']['q']))
    arima_fit = arima_model.fit(disp=0)

    # 提取ARIMA模型残差
    arima_residuals = pd.DataFrame(arima_fit.resid)
    arima_residuals.index = train_data.index[1:]

    # 提取移动平均值和标准差
    rolling_mean = train_data.rolling(window=window_size).mean()[window_size:]
    rolling_std = train_data.rolling(window=window_size).std()[window_size:]

    # 将ARIMA模型残差、移动平均值和标准差作为特征
    features = pd.concat([arima_residuals, rolling_mean, rolling_std], axis=1)
    targets = train_data.iloc[1:]

    # 对每个时间序列分割进行交叉验证
    rmse_scores = []
    for train_index, test_index in tscv.split(train_data):
        # 定义训练集和测试集
        X_train, X_test = features.iloc[train_index], features.iloc[test_index]
        y_train, y_test = targets.iloc[train_index], targets.iloc[test_index]

        # 拟合XGBoost模型
        xgb_model.fit(X_train, y_train)

        # 预测测试集
        y_pred = xgb_model.predict(X_test)

        # 计算RMSE
        rmse = np.sqrt(mean_squared_error(y_test, y_pred))
        rmse_scores.append(rmse)

    # 计算平均RMSE
    mean_rmse = np.mean(rmse_scores)

    # 更新最佳模型参数和最小RMSE
    if mean_rmse < min_rmse:
        best_params = params
        min_rmse = mean_rmse

# 输出最佳模型参数和最小RMSE
print('Best params:', best_params)
print('Min RMSE:', min_rmse)

最后，我们可以使用最佳参数训练XGBoost模型，并在测试集上进行预测。

# 定义XGBoost模型和ARIMA模型
xgb_model = xgb.XGBRegressor(**best_params['xgb_params'])
arima_model = ARIMA(train_data, order=(best_params['arima_params']['p'], best_params['arima_params']['d'], best_params['arima_params']['q']))
arima_fit = arima_model.fit(disp=0)

# 提取ARIMA模型残差
arima_residuals = pd.DataFrame(arima_fit.resid)
arima_residuals.index = train_data.index[1:]

# 提取移动平均值和标准差
rolling_mean = train_data.rolling(window=window_size).mean()[window_size:]
rolling_std = train_data.rolling(window=window_size).std()[window_size:]

# 将ARIMA模型残差、移动平均值和标准差作为特征
train_features = pd.concat([arima_residuals, rolling_mean, rolling_std], axis=1)
train_targets = train_data.iloc[1:]

# 拟合XGBoost模型
xgb_model.fit(train_features, train_targets)

# 对测试集进行预测
test_arima_residuals = pd.DataFrame(arima_fit.forecast(steps=len(test_data))[0]).diff()[1:]
test_rolling_mean = test_data.rolling(window=window_size).mean()[window_size:]
test_rolling_std = test_data.rolling(window=window_size).std()[window_size:]
test_features = pd.concat([test_arima_residuals, test_rolling_mean, test_rolling_std], axis=1)
test_targets = test_data.iloc[1:]
test_pred = xgb_model.predict(test_features)

# 计算测试集RMSE
test_rmse = np.sqrt(mean_squared_error(test_targets, test_pred))
print('Test RMSE:', test_rmse)