# Quant Time Series CFAI Page 428 Question 17 B

Sorry if this has been posted (didn’t find anything) and also checked errata. It asks, “if sales grew by 1 percent last quarter and by 2 percent four quarters ago, use the model to predict the sales growth for the quarter.” Now, they plug in these sales growth numbers directly into the formula, but do you think they forgot to incorporate the natural log of these numbers?

natural log would be required if they gave you actual numbers … e.g. Sales was 100 Mill in Q1, 120 Million in Q2. e.g. then you need to do log 120 - log 100 to find the growth rate. here they have given you the growth percent directly… or am I running up the wrong tree here?

cp, that was what I was thinking, but notice the way they apply it in the formula in the answer. I think the approach should be how you’ve explained it, i.e. taking the log of actual sales numbers and not with what they’ve done. It would be correct if they weren’t using natural logs in constructing their regression equation.

Correct. The log(change in sales) was given in growth percentage. So we need to substitute those sales growth percentages in decimal terms to get the ans.

You sure about that? ln (change in sales) isn’t mathematically equivalent to ln(sales t) - ln( sales t-1)

Or put more simply, ln (change in sales) != change in ln(sales)

I meant delta(ln(sales t) - ln(sales t-1)) = sales growth in decimal Thats what I would have done in the exam. And as CPK said, if sales were given like 100m, and 200m then would need to take the log of each sales and then take the difference to get the delta and then substitute to get the ans

Fair enough, a little ambiguous though, don’t you think? Sales growth to me implies somethinh analogous to stock growth, i.e. (sales t - sales t-1 / sales t-1) And by writing that I just figured it out… Page 284, footnote: delta ln ( x) is approximately equal to delta x / x Thanks guys…

ln(Sales t-1) - ln (Sales t-2) is what we need. i.e delta ln(Sales) They gave sales growth = (Sales t-1 - Sales t-2)/ Sales t-1 = delta(Sales)/ Sales = 0.01 Hence Note2 did the trick!