p. 424, #11a This is an example of a graph of ln (sales), and appears to trend upward over time. From the answer: A series that trends upward or downward over time often has a unit root and is not covariance stationary. ** -->>What exactly is covariance stationary? <>“Therefore, using an AR(1) regression on the undifferenced series is probably not correct.” <
for covariance stationary: - think sinus or cosine curve. - constant and finite mean, variance, and covariance of time series with itself has to be finite and constant to differentiate a ts: the price of your stock is: 100, 105, 103, 99, 101, 103, 106, 108, 112, … first order difference is 5, -2, -4, 2 … if you plot it against time you will see that the time series exhibits no up or downtrend, whereas the regular ts (not differentiated) goes up and down like crazy… note. if the first order difference is not stationary, then difference it again until you get a covariance stationary series.
rule in autoregressive time series is that the model must be covariance stationary and mean reverting. if it isn;t then the model is invalid. if there is a unit root problem then the solution is first differencing. A unit root problem is when the gradient coeffificent ie b1=1. Usually this coefficient will be less than one. if you look back at previous examples you’ll probably notice this. this means that the model isn’t mean reverting, or rather that the mean reverting level is undefined. The mean reverting formula is b0/(1-b1). so if b1=1, then this formula doesn’t make sense/it doesnt work. this is a unit root problem. its all jargon at the end of the day, you just need to learn it. Just remember that a unit root problem is something that might happen in an autogressive time model. if it does then you need to use first differencing.
b1 can’t be bigger than 1 for it to be covariance stationary in AR models, right?