Chapter 1 discussion question

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In class, we saw results for ARMA models fitted to two different time intervals. Here are the full R fitted model summaries for data up to 2018 and 2020:

y <- read.table(file="ann_arbor_weather.csv",header=1)
arma2018 <- arima(y$Low[y$Year<=2018], order=c(1,0,1))
arma2018

## 
## Call:
## arima(x = y$Low[y$Year <= 2018], order = c(1, 0, 1))
## 
## Coefficients:
##          ar1      ma1  intercept
##       0.8257  -0.7881    -2.8193
## s.e.  0.2650   0.2866     0.8080
## 
## sigma^2 estimated as 53.06:  log likelihood = -401.76,  aic = 811.52

arma2020 <- arima(y$Low[y$Year<=2020], order=c(1,0,1))
arma2020

## 
## Call:
## arima(x = y$Low[y$Year <= 2020], order = c(1, 0, 1))
## 
## Coefficients:
##           ar1      ma1  intercept
##       -0.0005  -0.0005    -2.8086
## s.e.  13.1214  13.2431     0.6842
## 
## sigma^2 estimated as 56.16:  log likelihood = -411.97,  aic = 831.93

What do you conclude by comparing these fitted models? Do you notice anything surprising?

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