Random Walks

When a time series which is a random walk is modeled as an AR(1) process, the resulting coefficients will be close to:

Incorrect. This describes a process in which the next period's value is always 1 plus some error term, regardless of the prior value.

Incorrect. These are the regression coefficients when a first difference variable from a random walk is modeled as an AR(1) process, but not the coefficients from modeling the original random walk as an AR(1).

Correct! This is a random walk, without a drift. The $$b_{1}$$ estimate of 1 suggests starting with the prior observed value. Nothing is added to this prior value in each period other than an error term, which is expected to be zero.

$$ b_0 = 1 $$, and $$ b_1 = 0 $$.

$$ b_0 = 0 $$, and $$ b_1 = 0 $$.

$$ b_0 = 0 $$, and $$ b_1 = 1 $$.