Module 9.1 LOS 9.a: Forecasting with an AR model

The simplest form of a linear trend is:

yt = b0 + b1(t) + εt


y= the value of the time series (the dependent variable) at time t

b= intercept at the vertical axis (y-axis)

b= slope coefficient (or trend coefficient)

ε= 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.

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