Random walk with or without drift

CFA Level II
#1

Do all time series models with random walk (with or without drift) claim to have a regression coefficients of 1? The book is explaining how AR models may be invalid for these types of data since they will not be covariance stationary (since it assumes the regression coefficients are 1).

Thanks!

#2

Be careful about your terminology.

In a random walk,

x(i+1) = _b_0 + _b_1 × xi

Both _b_0 and _b_1 are regression coefficients; however, _b_1 is a slope coefficient, while _b_0 is not.

In any case, in a random walk, _b_1 = 1. If _b_0 = 0, it is a random walk without drift, and if _b_0 ≠ 0, it is a random walk with drift.