在时间序列分析中,首先遇到的问题就是关于数据的平稳性问题。
定义
![](https://img.haomeiwen.com/i11013023/c002255ddc73fdbc.png)
关于随机过程,可见 时间序列|AR、MA、ARMA、ARIMA
一、若干概念
(一)白噪声
![](https://img.haomeiwen.com/i11013023/dc4f3b6e99b02a58.png)
(二)随机游走
![](https://img.haomeiwen.com/i11013023/2b493282751bfa1c.png)
(三)差分处理
![](https://img.haomeiwen.com/i11013023/327b1ec6cb23bf47.png)
二、平稳性判断
(一)图示法
给出一个随机时间序列,首先可通过该序列的时间路径图来粗略地判断它是否是平稳的。
- 一个平稳的时间序列在图形上往往表现出一种围绕其均值不断波动的过程
-
非平稳序列则往往表现出在不同的时间段具有不同的均值(如持续上升或持续下降)
图示法
(二)ACF法
![](https://img.haomeiwen.com/i11013023/7df999f4ce5556b8.png)
![](https://img.haomeiwen.com/i11013023/0eeaf85d9e438bff.png)
![](https://img.haomeiwen.com/i11013023/dae3fcf52bb7f2a3.png)
![](https://img.haomeiwen.com/i11013023/6c10005f7d57ff00.png)
例子
![](https://img.haomeiwen.com/i11013023/fdc24f5a065b2d82.png)
** 序列Random1一纯随机序列**
![](https://img.haomeiwen.com/i11013023/d705f8daa8c9ec61.png)
** 序列Random2一随机游走过程**
![](https://img.haomeiwen.com/i11013023/08350000c47c259f.png)
![](https://img.haomeiwen.com/i11013023/03628358ca91157d.png)
(三)单位根法
1.DF检验
![](https://img.haomeiwen.com/i11013023/02013a99cc1201aa.png)
![](https://img.haomeiwen.com/i11013023/abd455ce1e0c6ba8.png)
![](https://img.haomeiwen.com/i11013023/13fd36dde22b851d.png)
![](https://img.haomeiwen.com/i11013023/25d20450ddb144ac.png)
![](https://img.haomeiwen.com/i11013023/c64d0676274b6485.png)
2.ADF检验
![](https://img.haomeiwen.com/i11013023/c178931923492640.png)
![](https://img.haomeiwen.com/i11013023/813f2d80376e7e93.png)
![](https://img.haomeiwen.com/i11013023/2744d0355ee0d881.png)
![](https://img.haomeiwen.com/i11013023/1fec601649684ef7.png)
![](https://img.haomeiwen.com/i11013023/0012ffd991fd4604.png)
示例
![](https://img.haomeiwen.com/i11013023/dde2380f070135ca.png)
![](https://img.haomeiwen.com/i11013023/6b7cef96794ab7ac.png)
![](https://img.haomeiwen.com/i11013023/becbf687788ed798.png)
参考资料
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