### TIME SERIES - CLIMATE CHANGE:

Basically, a reproduction of this post in R-bloggers.

The model is not stationary. The criteria for a stationary process are:

```
1. Constant mean across time.
2. Constant variance across time.
3. Variance between observations only depends on distance (lag).
```

The variance may be constant, but the mean increases with time.

This can be assessed by observing the number of significant correlations:

```
par(mfrow=c(1,2))
acf(gtemp)
pacf(gtemp)
```

We can make this series stationary by differencing:

`## Loading required package: tseries`

`adf.test(diff(gtemp), alternative="stationary", k=0)`

```
##
## Augmented Dickey-Fuller Test
##
## data: diff(gtemp)
## Dickey-Fuller = -15.158, Lag order = 0, p-value = 0.01
## alternative hypothesis: stationary
```

```
par(mfrow = c(1,2))
acf(diff(gtemp))
pacf(diff(gtemp))
```

We can try AR of \(4\) and MA of \(1\):

```
fit1 = Arima(gtemp, order = c(4,1,1), include.drift = T)
future = forecast(fit1, h = 50)
plot(future)
```

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