I cannot understand the following problem: Schweser Time Series Question 8 on Page 255 An analyst has determined that monthly sales have been increasing over the last 10 years, but the growth rate over the period has been relatively constant. Which model is most appropriate to predict future sales? I think that a constant growth rate calls for a linear model. In my understanding constant is equal to linear. But Schweser wants you to use a log model ln (sales). Why is that? As far as my understanding goes, log model only apply to potential growth but not to constant growth. Please clarify. Thank you

if you went with a log linear model – you are basically doing ln (sales t / sales (t-1)) and that automatically takes care of the period… growth rate here is sales t / sales t-1 and not difference of [sales t - (sales t-1)] so log model is more appropriate.

I don’t get that. growth rate here is sales t / sales t-1 and not difference of [sales t - (sales t-1)] This fact seems obvious. Let’s say that sales t / sales t-1 = 1.1 (10% growth) In this case, b1 would simply be 1.1. Am I missing a key takeaway from this study session?

your independent variable is increasing in terms of 1 unit (for each time period) and your dependent variable has a multiplication effect (the 10% growth rate) one is linear increase, other is log linear (bcos of the multiplication involved). not explaining it very well here… probably wyantjs or jdv can add on… it has to be log linear – to ensure that the multiplication got converted to an addition - that much I know… another way of saying the same thing… if you plotted the dependent variable against the independent variable - you would not get a straight line. but if you plotted the log (salest/sales t-1) against t - you will get a straight line.

Well, that’s exactly the point i don’t get. If the industry is growing at constant rate, the plot must be a straight line and not a exponential function. Constant growth implies (to me) that a constant b1 is linked to the time variable and leads to an linear increase. If you have a constant increase from one period to another the growth is exponential as asking for a log model since there is a compounding effect. But as far as I understand this problem, the growth is constant to the base period (->linear) and not constant to the previous period (-> exponential). The question text says that the growth for the period was constant, let’s say 10%. This would imply that the CAGR of the period is 10%, right? Whether this CAGR was achieved by constant or exponential growth model still remains unsolved. What’s the point i’m missing here?

If your industry is growing at a constant AMOUNT it it a linear relationship (so say for example, a 1 unit change in independent variable makes a $10 increase in dependent variable) If your industry is growing at a constant RATE it it a log-linear relationship (so say for example, a 1 unit change in independent variable makes a 10% increase in dependent variable). Note here the compounding effect, it is 10% on y-1, that is exponential growth that will plot as a straight line if i take the log of both sides of the following equation: y = exp (bo + b*t) logy = bo + b1*t the key is the difference in terminology (CONSTANT RATE VS CONSTANT DOLLAR AMOUNT)

understood now! thanks Aliman.

it comes down to independent variable here is t, so we need to do log linear

if independent variable is yt-1, then it will be linear model

yt = yt-1 * (1+growth_rate)