P. 432, Quants, example 12.
Original series: lnSalest = b0 + b1lnSalest-1 + errort
Unit root suspected, so he takes the first difference by subtracting lnSalest-1 from both sides for the test. The book then gets:
lnSalest - lnSalest-1 = b0 + b1[lnSalest-1 - lnSalest-2] + errort
Can anybody please show the steps that take the original equation to the second? If I’m not mistaken, it seems to imply b1lnSalest-2 = lnSalest-1
How?
Help would be much appreciated, thanks.
assuming the original dependet variable is LnSales, the first difference will be LnSales(t-1).
However, in this case, since the independent variable was already lagged by one year period (LnSalest-1), finding the second difference (AR2) or finding the first difference for LnSales(t-1) will be LnSales(t-2).
t=present period, t-1 = last year, t-2= 2 years ago, thus first difference of LnSales(t-1) = LnSales(t-2).
If you are to find the second difference AR(2) for LnSales(t-1), it will be LnSales(t-3).
They’re not taking the second difference, and your post is a little unlcear.
All they are doing is taking the observation at time (T) and subtracting the observation from the period before, (T-1). They are doing this for every observation, which transforms the variables into a difference between observations that are one period apart (suspected AR1).
(lnSalest - lnSalest-1) = b0 + b1**(lnSalest-1 - lnSalest-2)** + errort
(Assuming they didn’t just run a first difference program) To arrive here, they went back to the data set and subtracted the observation from time period 9 from time period 10, time period 8 from time period 9,… for all observations. Then the refit the model with the new difference “variables”. There aren’t any really crazy steps to transform the equation.
Hope this helps!
Uhhhhhh, better defer this one the the magician cause I don’t even know what you’re talking about. I wouldn’t get too caught up in L2 quant because it is painful but not heavily weighted. I was fairly weak in quant & still got > 70%.