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# 0x04 拟合度量方法

## 拟合度量

对于建立的时间序列模型, 常见的如ARIMA模型, 模型的质量如何, 评价方法需要考虑以下几个方面:

* 模型对数据集的描述能力, 体现了模型的拟合程度和预测准确的能力
* 模型本身的复杂度, 相同预测结果, 更简单的模型更合适

综合以上两者, 常用下面的几种方法对模型进行评价.

## AIC

**AIC, Akaike information criterion, 赤池信息量**:

$$AIC=2k-2\ln{L}$$

其中$$k$$模型变量的个数, 对于ARIMA模型, 就是`p+q`的值; $$L$$是损失函数, 通常使用**MSE**, 这在回归分析中有介绍, **MSE**即是**均方残差**, 即残差平方和除以对应的自由度, 是拟合结果与实际观测值之间差距的平方之和.

## BIC

**BIC, Bayesian information criterion, 贝叶斯信息量**:

$$BIC=\ln(n)k-2\ln{L}$$

使用**BIC**的优势在于: 在维数过大且训练样本数据相对较少的情况下, 可以有效避免出现维度灾难现象.

## AIC/BIC与Python

使用:

```python
from statsmodels.tsa.arima_model import ARIMA
```

模型得到的`statsmodels.tsa.arima.ARIMAResults`结果对象中, 包含了这两种度量方法拟合后的结果值. 可以使用这种度量, 对不同参数的ARIMA模型进行评价, 从中选取最好的模型来使用.


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