time_seriers.Rmd

---
title: "time seriers"
output: html_document
---


```{r,echo=FALSE}
library(TSA)
x=read.table(file="C:\\Users\\TSR\\Desktop\\共享資料\\4444.txt")

cc=x$V3
cc

###原型
plot.ts(cc,type="o")
acf(cc)
pacf(cc)
####
```

####從acf上看起來每4筆有季節效應，所以先處理季節效應

```{r}
###處理季節效應
cc1=diff(log(cc),lag=4)
plot.ts(cc1)

acf(cc1,lag.max=30)

pacf(cc1,lag.max=30)
eacf(cc1)
```
####acf看起來像是指數遞減，pacf有明顯的5根
####所以先從(5,0,0)x(0,1,0)開始嘗試
```{r}
mse=list()
###ar5
m1=arima(cc,order=c(5,0,0),seasonal=list(order=c(0,1,0),period=4))
m1
fitted(m1)
plot(cc,col="red",type="l")
lines(fitted(m1),col="blue")
p1=c(170,170)
p2=c(18,20)
t=c("red:原有數列","blue:fit數列")
text(p1,p2,labels=t,col = c("red","blue"))

plot(rstandard(m1))
abline(h=c(2,-2))

qqnorm(rstandard(m1))
qqline(rstandard(m1))

acf(rstandard(m1))
pacf(rstandard(m1))
plot(m1,n.ahead=20,type='b')


mse[1][1]=sum((unlist(m1[8]))^2)/length(cc)
```
####殘差都在容許的範圍之內
####但是ar3的係數可能為0,所以試試看(2,0,0)X(0,1,0)

```{r}
####
m1=arima(cc,order=c(2,0,0),seasonal=list(order=c(0,1,0),period=4))
m1
plot.ts(cc,col="red")
lines(fitted(m1),col="blue")
text(p1,p2,labels=t,col = c("red","blue"))
plot(rstandard(m1))
abline(h=c(2,-2))

qqnorm(rstandard(m1))
qqline(rstandard(m1))

acf(rstandard(m1))
pacf(rstandard(m1))

plot(m1,n.ahead=4,type='b')
mse[[1]][2]=sum((unlist(m1[8]))^2)/length(cc)
```
####從殘差上看起來，估計的蠻差的，故仍選擇(5,0,0)X(0,1,0)


#分段#
####由於此時間序列前半段有上升趨勢，後半段平穩，故考慮將前後分開討論
```{r}
p1=c(80,80)
p2=c(18,20)

cc=x$V3
cc1=cc[1:95]
cc2=cc[96:196]

plot.ts(cc1,type="o")


acf(cc1)
pacf(cc1)
```
####從acf看起來每隔4個時期有季節效應
####故先處理季節效應
```{r}
cc1=diff(cc1,lag=4)

plot.ts(cc1)

acf(cc1)
pacf(cc1)
```
####acf 看起來像指數遞減，但是pacf第一根突出所以猜測是ar1
####但是第四根也凸出，所以猜測在季節上有ar1

```{r}
cc=x$V3
cc1=cc[1:95]
cc2=cc[96:196]


##季節性

m1=arima(cc1,order=c(1,0,0),seasonal=list(order=c(1,1,0),period=4))
m1

plot.ts(cc1,col="red")
lines(fitted(m1),col="blue")
text(p1,p2,labels=t,col = c("red","blue"))
plot(rstandard(m1))
abline(h=c(2,-2))

qqnorm(rstandard(m1))
qqline(rstandard(m1))

acf(rstandard(m1))
pacf(rstandard(m1))
plot(m1,n.ahead=20,type='b')

mse[2][1]=sum((unlist(m1[8]))^2)/length(cc1)
```
####殘差大致都在可行範圍之內
####所以判定 (1,0,0)X(1,1,0) 為一個可行的模型
####下面在利用上面做出的(5,0,0)X(0,1,0)做預測
```{r}
cc=x$V3
cc1=cc[1:95]
cc2=cc[96:196]
##原模型
m1=arima(cc1,order=c(5,0,0),seasonal=list(order=c(0,1,0),period=4)　)
m1

plot.ts(cc1,col="red")
lines(fitted(m1),col="blue")
text(p1,p2,labels=t,col = c("red","blue"))
plot(rstandard(m1))
abline(h=c(2,-2))

qqnorm(rstandard(m1))
qqline(rstandard(m1))

acf(rstandard(m1))
pacf(rstandard(m1))
plot(m1,n.ahead=20,type='b')

mse[[2]][2]=sum((unlist(m1[8]))^2)/length(cc1)

```


##後段##
```{r}
p1=c(90,90)
p2=c(26,27)
cc2=cc[96:196]
plot.ts(cc2,type="o")
acf(cc2)
pacf(cc2)
```
####看起來每4期有相關，先處理季節效應
```{r}
cc2=diff(cc2,lag=4)
plot.ts(cc2)
acf(cc2)
pacf(cc2)
```
####因acf還是很多呈現相關，判定為非平穩，故再diff一次
```{r}
cc2=diff(cc2)
plot.ts(cc2)
acf(cc2)
pacf(cc2)
```
差分後的acf pacf都在4有一根，所以季節性的模型為(1,1,1) s=4 ,acf pacf 的第一根也是突出，故用(1,1,1)配，整體為(1,1,1)x(1,1,1) s=4
```{r}
cc1=cc[1:95]
cc2=cc[96:196]

m1=arima(cc2,order=c(1,1,1),seasonal=list(order=c(1,1,1),period=4))
plot.ts(cc2,col="red")
lines(fitted(m1),col="blue")

text(p1,p2,labels=t,col = c("red","blue"))
plot(rstandard(m1))
abline(h=c(2,-2))

qqnorm(rstandard(m1))
qqline(rstandard(m1))

acf(rstandard(m1))
pacf(rstandard(m1))
plot(m1,n.ahead=20,type='b')

mse[3][1]=sum((unlist(m1[8]))^2)/length(cc2)

```

####再度利用原本(5,0,0)x(0,1,0) s=4做預測
```{r}
##原模型
m1=arima(cc2,order=c(5,0,0),seasonal=list(order=c(0,1,0),period=4))
m1


plot.ts(cc2,col="red")
lines(fitted(m1),col="blue")

text(p1,p2,labels=t,col = c("red","blue"))
plot(rstandard(m1))
abline(h=c(2,-2))

qqnorm(rstandard(m1))
qqline(rstandard(m1))

acf(rstandard(m1))
pacf(rstandard(m1))
plot(m1,n.ahead=20,type='b')

mse[[3]][3]=sum((unlist(m1[8]))^2)/length(cc2)
mse
```