As mentioned before, a time series must be stationary for it to be used to predict well founded values. We will go over several models that we can create in order to allow forecasting.

Please note that the first 3 models we cover, AR, MA, and ARMA, can be used on already stationary time series in order to allow them to predict better values. The remaining models are used on non-stationary time series.

Two of the most common models in time series are the Autoregressive (AR) models and the Moving Average (MA) models.

Autoregressive Model: AR(p)

The autoregressive model uses observations from preivous time steps as input to a regression equations to predict the value at the next step. The AR model takes in one argument, p, which determines how many previous time steps will be inputted.

The order, p, of the autoregressive model can be deterimined by looking at the partial autocorrelation function (PACF). The PACF gives the partial correlation of a stationary time series with its own lagged values, regressed of the time series at all shorter lags.

Let鈥檚 take a look at the PACF plot for the global temperature time series using the pacf() function in R.