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
![11013023-c002255ddc73fdbc.png](https://upload-images.jianshu.io/upload_images/11013023-c002255ddc73fdbc.png)
定义
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
![11013023-dc4f3b6e99b02a58.png](https://upload-images.jianshu.io/upload_images/11013023-dc4f3b6e99b02a58.png)
白噪声
(二)随机游走
![11013023-2b493282751bfa1c.png](https://upload-images.jianshu.io/upload_images/11013023-2b493282751bfa1c.png)
随机游走
(三)差分处理
![11013023-327b1ec6cb23bf47.png](https://upload-images.jianshu.io/upload_images/11013023-327b1ec6cb23bf47.png)
差分处理
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
![11013023-7df999f4ce5556b8.png](https://upload-images.jianshu.io/upload_images/11013023-7df999f4ce5556b8.png)
ACF1
![11013023-0eeaf85d9e438bff.png](https://upload-images.jianshu.io/upload_images/11013023-0eeaf85d9e438bff.png)
ACF2
![11013023-dae3fcf52bb7f2a3.png](https://upload-images.jianshu.io/upload_images/11013023-dae3fcf52bb7f2a3.png)
ACF3
![11013023-6c10005f7d57ff00.png](https://upload-images.jianshu.io/upload_images/11013023-6c10005f7d57ff00.png)
ACF4
例子
![11013023-fdc24f5a065b2d82.png](https://upload-images.jianshu.io/upload_images/11013023-fdc24f5a065b2d82.png)
case1
** 序列Random1一纯随机序列**
![11013023-d705f8daa8c9ec61.png](https://upload-images.jianshu.io/upload_images/11013023-d705f8daa8c9ec61.png)
case2
** 序列Random2一随机游走过程**
![11013023-08350000c47c259f.png](https://upload-images.jianshu.io/upload_images/11013023-08350000c47c259f.png)
case3
![11013023-03628358ca91157d.png](https://upload-images.jianshu.io/upload_images/11013023-03628358ca91157d.png)
case4
(三)单位根法
1.DF检验
![11013023-02013a99cc1201aa.png](https://upload-images.jianshu.io/upload_images/11013023-02013a99cc1201aa.png)
DF1
![11013023-abd455ce1e0c6ba8.png](https://upload-images.jianshu.io/upload_images/11013023-abd455ce1e0c6ba8.png)
DF2
![11013023-13fd36dde22b851d.png](https://upload-images.jianshu.io/upload_images/11013023-13fd36dde22b851d.png)
DF3
![11013023-25d20450ddb144ac.png](https://upload-images.jianshu.io/upload_images/11013023-25d20450ddb144ac.png)
DF4
![11013023-c64d0676274b6485.png](https://upload-images.jianshu.io/upload_images/11013023-c64d0676274b6485.png)
DF5
2.ADF检验
![11013023-c178931923492640.png](https://upload-images.jianshu.io/upload_images/11013023-c178931923492640.png)
ADF1
![11013023-813f2d80376e7e93.png](https://upload-images.jianshu.io/upload_images/11013023-813f2d80376e7e93.png)
ADF2
![11013023-2744d0355ee0d881.png](https://upload-images.jianshu.io/upload_images/11013023-2744d0355ee0d881.png)
ADF3
![11013023-1fec601649684ef7.png](https://upload-images.jianshu.io/upload_images/11013023-1fec601649684ef7.png)
ADF4
![11013023-0012ffd991fd4604.png](https://upload-images.jianshu.io/upload_images/11013023-0012ffd991fd4604.png)
ADF5
示例
![11013023-dde2380f070135ca.png](https://upload-images.jianshu.io/upload_images/11013023-dde2380f070135ca.png)
1
![11013023-6b7cef96794ab7ac.png](https://upload-images.jianshu.io/upload_images/11013023-6b7cef96794ab7ac.png)
2
![11013023-becbf687788ed798.png](https://upload-images.jianshu.io/upload_images/11013023-becbf687788ed798.png)
3
参考资料