From Qbank Barry Phillips, CFA, has estimated an AR(1) relationship (xt = b0 + b1×xt-1 + et) and got the following result: xt+1 = 0.5 + 1.3×xt + et. Phillips should: A) first difference the data because b1=1.3 > 1. B) not first difference the data because b0=0.5 < 1. C) not first difference the data because b1 - b0 = 1.3 - 0.5 = 0.8 < 1. D) first difference the data because b0=0.5 < 1. The correct answer was A. The condition b1=1.3 > 1 means that the series has a unit root and is not stationary. The correct way to transform the data in such an instance is to first difference the data.
I thought we only have unit root if b1=1, also from qbank LOS it says LOS Explanation Along with having a defined mean-reverting level, a requirement for covariance stationarity in a time series that is described by an AR(1) model is that the absolute value of the coefficient on the lag variable must be less than one. If the value of the lag coefficient is equal to one, the time series is a random walk, and it is said to have a unit root. If the absolute value of the lag coefficient is greater than one, the time series is said to have an explosive root. Do we suppose to know about this “explosive root” crap? I searched through the notes and I can’t find it being mentioned anywhere.
if the coefficient on the lagged independent variable is grater than 1, its not covariance stationary. Think about it this way…if you are modeling retail sales and you use last month’s sales as your lagged coefficient, and the beta is greate than 1, you will always have greater sales at time t+1. Not good.
but the B0 can be negative, right? I am so confused now :S
avnx Wrote: ------------------------------------------------------- > but the B0 can be negative, right? > > I am so confused now :S So you mean to say that the value of sales at time t=0 will be Negative? (as per jb’s example?)
I don’t know about the terminology “explosive root”, but it’s clearly not stationary. As jb points out, you would get explosive growth. Note that you expect that X(t) = 1.3^t*X0 +[other stuff]. That’s exponential growth which is about as non-stationary as you get. For lots of time series, it makes tons of sense for b0 to be negative just as in regular regressions.
OK I guess I will just B1 has to be < 1 or else there is a problem. I hope they don’t test quant in depth, right now I can handle most of the questions but clearly have little understanding of the material.