Mod8P2

temp<-read.table("temp.txt", header=T)
temp.ts<-ts(temp$temps, frequency=12) #create monthly time series
plot(temp.ts)
library(TTR)

## Warning: package 'TTR' was built under R version 4.3.2

temp.ma<-SMA(temp.ts, n = 5)
lines(temp.ma, col="red", lwd=2)

temp.decomp<-decompose(temp.ts)
plot(temp.decomp)

acf(temp.ts)

acf(temp.decomp$random[!is.na(temp.decomp$random)])

pacf(temp.ts)

library(forecast)

## Warning: package 'forecast' was built under R version 4.3.2

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

temp.fit<-auto.arima(temp.ts)
summary(temp.fit)

## Series: temp.ts 
## ARIMA(0,0,1)(2,1,0)[12] 
## 
## Coefficients:
##          ma1     sar1     sar2
##       0.2456  -0.5212  -0.3233
## s.e.  0.0774   0.0823   0.0827
## 
## sigma^2 = 3.772:  log likelihood = -300.76
## AIC=609.52   AICc=609.81   BIC=621.4
## 
## Training set error measures:
##                     ME     RMSE      MAE       MPE     MAPE      MASE
## Training set 0.2384692 1.846384 1.498262 0.2682136 11.90101 0.8327783
##                     ACF1
## Training set 0.005413047

checkresiduals(temp.fit)

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(0,0,1)(2,1,0)[12]
## Q* = 38.688, df = 21, p-value = 0.01069
## 
## Model df: 3.   Total lags used: 24

temp.fcast<-forecast(temp.fit)
plot(temp.fcast)