The simplest form of a linear trend is:
yt = b0 + b1(t) + εt
yt = the value of the time series (the dependent variable) at time t
b0 = intercept at the vertical axis (y-axis)
b1 = slope coefficient (or trend coefficient)
εt = error term (or residual term or disturbance term)
t = time (the independent variable); t = 1, 2, 3…T
We can predict values by plugging the coefficients with our time period, similar to a regular regression model forecast. However, the difference for an AR model is that we calculate the values for each period we are forecasting, creating a table of values.
A variation of this model would be the log-linear model.