The simplest form of a linear trend is:

y_{t} = b_{0} +
b_{1}(t) + ε_{t}

where:

y_{t }= the value of
the time series (the dependent variable) at time t

b_{0 }= intercept at
the vertical axis (y-axis)

b_{1 }= slope
coefficient (or trend coefficient)

ε_{t }= 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.