采用ARMA-GARCH模型对碳交易价格波动率进行样本内预测的python代码
时间: 2024-10-08 20:12:43 浏览: 81
ARMA-GARCH模型是一种结合自回归移动平均(ARMA)模型和广义自回归条件异方差(GARCH)模型的技术,用于捕捉金融时间序列数据中的趋势、季节性和波动性。在Python中,我们可以使用`pandas`, `statsmodels`以及`pykalman`库来构建和预测ARMA-GARCH模型。
以下是一个简单的例子,展示了如何使用` statsmodels.tsa.statespace`模块对碳交易价格波动率进行预测:
```python
# 导入所需库
import pandas as pd
from statsmodels.tsa.stattools import adfuller
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
from statsmodels.tsa.arima_model import ARIMA
from statsmodels.tsa.garch import GARCH, EGARCH
import matplotlib.pyplot as plt
# 假设df是包含碳交易价格的数据框,'price'列是我们关注的价格系列,'volatility'是波动率计算后的结果
data = df['price']
# 检查 Stationarity
result_adf = adfuller(data)
print(f"ADF Statistic: {result_adf[0]}")
if result_adf[1] > 0.05: # 如果ADF统计显著,通常需要差分
data_diff = data.diff().dropna()
else:
data_diff = data
# 分析自相关和偏自相关图
plot_acf(data_diff)
plot_pacf(data_diff)
plt.show()
# 构建ARIMA模型
arima_model = ARIMA(data_diff, order=(p, d, q)) # 这里的(p, d, q)需要根据ACF和PACF图来选择
arima_results = arima_model.fit(disp=0)
# 计算GARCH成分
garch_model = GARCH(p, q)(arima_results.resid)
egarch_model = EGARCH(p, q)(arima_results.resid) # 或者使用EGARCH如果需要考虑对数正态分布
# 预测波动率
forecast_volatility_arima = arima_results.forecast(steps=forecast_steps)[0]
forecast_volatility_garch = garch_model.forecast(steps=forecast_steps)[0]
forecast_volatility_egarch = egarch_model.forecast(steps=forecast_steps)[0]
# 结果展示
plt.figure(figsize=(10, 6))
plt.plot(forecast_volatility_arima, label='ARIMA')
plt.plot(forecast_volatility_garch, label='GARCH')
plt.plot(forecast_volatility_egarch, label='EGARCH')
plt.legend()
plt.title('Carbon Trading Price Volatility Forecast')
plt.xlabel('Steps Ahead')
plt.ylabel('Volatility')
plt.show()
阅读全文