时间序列预测
时间序列通常包含这些组成部分:线性趋势(Trend),季节变化(Seasonality),循环变化(Cycle),不规则变化(Irregularity)
多步预测的五种策略
可分为单步预测(one-step-ahead)和多步预测(muti-step-ahead)
多步预测的五种策略:
- recursive (or iterated) strategy
![在这里插入图片描述](https://img-blog.csdnimg.cn/20200201231751338.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2l0bmVyZA==,size_16,color_FFFFFF,t_70)
- direct strategy
![在这里插入图片描述](https://img-blog.csdnimg.cn/20200201231759105.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2l0bmVyZA==,size_16,color_FFFFFF,t_70)
- combination of both the recursive and direct strategies, called DirREC
![在这里插入图片描述](https://img-blog.csdnimg.cn/20200201231825199.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2l0bmVyZA==,size_16,color_FFFFFF,t_70)
- the Multi-Input Multi-Output (MIMO) strategy
![在这里插入图片描述](https://img-blog.csdnimg.cn/20200201231839220.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2l0bmVyZA==,size_16,color_FFFFFF,t_70)
- DirMO strategy
![在这里插入图片描述](https://img-blog.csdnimg.cn/20200201231850905.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2l0bmVyZA==,size_16,color_FFFFFF,t_70)
常用指标
y^ 为预测值,
y 为实际值,
N 为预测数:
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MSE
MSE=N1i=1∑N(y^i−yi)2
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RMSE
RMSE=N1i=1∑N(y^i−yi)2
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NMSE
NMSE=N⋅σy21i=1∑N(y^i−yi)2
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MAE
MAE=N1i=1∑N∣y^i−yi∣
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MAPE
MAPE=N1i=1∑N∣∣∣∣yiy^i−yi∣∣∣∣
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sMAPE
symmetric mean absolute percentage error
sMAPE=N1i=1∑N∣∣∣∣(y^i+yi)/2y^i−yi∣∣∣∣
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MASE
mean absolute scaled error
MASE=l−p1∑i=p+1−l0∣y^i−yi−p∣h1∑i=1h∣y^i−yi∣其中
l 是训练集样本数,
h 是预测长度,
p 是季节长度