Predicting a value from the previous value
In a time series without trend, positive autocorrelation means that values tend to be followed by others of similar size.
We can try to predict yt from its previous value by fitting a straight line by least squares to this scatterplot,
yt = b0 + b1 yt−1
This is a type of auto-regressive model, and is usually called an AR(1) model.
Forecasting further into the future
The model only directly predicts one time period into the future,
t = b0 + b1 yt − 1
but we can predict further into the future using:
t + k = b0 + b1
t + k −1