I came across a problem in Schweser where I was given a linear trend model with no direct inputs for the trend.
Specifically, the model = α + β × (Trend)t + ε
The coefficient for the intercept was provided as 10.0015 and the coefficient of the trend was provided as 6.74.
The problem also provided that “The Trend is 1,2,3,4,5,6,7,8,9,10,11,12.”
I was then asked to derive the forecast of sales for the first out-of-sample period. The answer was 10.0015 + (13 x 6.74) = 97.62
In previous problems I was provided the plug-in for the trend. For this problem you were seemingly supposed to figure out that 13 is the next number in the trend (Trend at time t = (t-1) + 1)? I made this conclusion myself because the answer explanation did not tell me where the 13 came from.
Am I correct with my conclusion as to where the 13 came from (obviously in the context of my previous paragraph)? Do we have to know how to derive the input for the trend (the figure to multiply with the coefficient) for the exam?
[Disclaimer: I suck at everything past the multiple regression readings in Quant and could be thinking about this entirely wrong]