- 数据来源: R语言自带 Nile 数据集(尼罗河流量)
- 分析工具:R-3.5.0 & Rstudio-1.1.453
#清理环境,加载包
rm(list=ls())
library(forecast)
library(tseries)
#趋势查看
plot(Nile)
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217165145446-717209540.png)
#平稳性检验
#自相关图
acf(Nile)
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217165344822-354192051.png)
#偏相关图
pacf(Nile)
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217165425735-392915430.png)
#也可以直接用tsdisplay查看
tsdisplay(Nile)
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217165605165-1522810818.png)
#单位根检验
adf.test(Nile)
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217170013742-941282237.png)
- 从自相关图上看,自相关系数没有快速衰减为0,呈拖尾,单位根检验进一步验证,存在单位根,所以序列为非平稳序列
#做序列差分
#可以用ndiffs判断需要做几阶差分
ndiffs(Nile)
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217170419608-950828306.png)
#做一阶差分,然后再进行检验
Nile_diff=diff(Nile,1)
plot(Nile_diff)
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217170912314-1164234738.png)
acf(Nile_diff)
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217170953963-1656861235.png)
pacf(Nile_diff)
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217171025403-1680731830.png)
adf.test(Nile_diff)
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217171055375-375075992.png)
#建立模型
(mod=arima(Nile,order=c(0,1,1),method='ML'))
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217171334172-1270790208.png)
#auto.arima通过选取AIC和BIC最小来选取模型,与根据acf和pacf图建立的模型进行比较
(mod_auto=auto.arima(Nile))
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217171721390-1781921788.png)
# 残差正态性检验
qqnorm(mod$residuals)
qqline(mod$residuals)
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217172003561-986970464.png)
qqnorm(mod_auto$residuals)
qqline(mod_auto$residuals)
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217172021197-1175203861.png)
# 残差白噪检验
Box.test(mod$residuals,type='Ljung-Box')
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217172048448-936771424.png)
Box.test(mod_auto$residuals,type='Ljung-Box')
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217172106741-323963996.png)
- 根据检验结果来看,还是选择根据acf图和pacf图建立的模型比较好
# 进行预测
(pre=forecast(mod,5))
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217172231072-1432798103.png)
plot(Nile,col='pink')
par(new=T)
plot(pre,col='green')
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217172609114-764147663.png)
plot(pre,col='green')
![](https://img2018.cnblogs.com/blog/1544813/201812/1544813-20181217173059388-649954938.png)