Slope Coefficient in Linear Regression

Can some one please help me understand why is the slope coefficient of a linear regression < 1 ? I understand that if the slope coefficient is 1, then we have a random walk. But can’t understand why can’t the slope coefficient be greater than 1?

First, you’re not talking about linear regression in general; you’re talking about an autoregressive model, and, specifically, an AR(1) model.

Second, it’s not true that the slope coefficient in an AR(1) model must be less than 1. What is true is that for an AR(1) model to have a mean reverting level, |b1| must be less than 1; i.e., −1 < b1 < 1.

If you want to see what happens when |b1| ≥ 1, create an Excel model of an AR(1) model with parameters b0 and b1. See what happens when you choose each of these values for b1:

  • −1.1
  • −1.0
  • −0.7
  • −0.4
  • −0.1
  • 0.0
  • 0.1
  • 0.4
  • 0.7
  • 1.0
  • 1.1

You’ll learn a lot more about AR(1) models by doing it yourself in Excel than by reading something that someone here writes.

note that the dependent scale is logarithmic.