# Covariance Stationary Question

Hi everyone, I’m just doing some question bank problems. In one of them, the slope coefficient was 1.09 or something like that. One question asked if there was a unit root, and it turned out that there was because the null that the slope = 1 could not be rejected. I understand that part. But then in another question in the item set having to do with first differencing the data, this was the answer: “Since the coefficient on the slope coefficient is greater than one, the process is not covariance stationary. A common technique to correct for this is to first difference the variable to perform the following regression: Δ(WPM)t = bo + b1 Δ(WPM)t-1 + ε t.” Now, my question: is that first sentence correct? Is it true that if the slope coefficient is greater than 1 it is not covariance stationary? I can’t find anything in the reading that says that. Can anyone confirm/explain? Thanks!

CFAI book 1 page 380 states that “if a time series comes from an AR(1) model, then to be covariance stationary the absolute value of the lag coefficient, b1, must be less than 1.0”. If it is equal to 1, its a random walk. If it is greater than 1, the series is not covariance stationary.

Slope coefficient >1 in a time series model is called an “explosive root”, and as the above guy says is not cov stat.

If it has a slope greater than one think of the line it will produce; it’s not a straight line, it’s a trend line. If the mean is always going to be increasing, it’s not covariance stationary.

Springahead is this a fact? scheswer does not mention this anywhere.

It is stated in the CFAI book 1 page 381.