If the forecasting model is well specified, then prediction errors from the model will not be serially correlated. If the prediction error for each period is not serially correlated then it follows that:
a) variance of the multiperiod forecast will be same as single period forecast, as required by one of the assumptions of Multi-variate regression (variance of errors is constant).
b) variance of the multiperiod forecast will be higher than the single period forecast.
c) variance of the multiperiod forecast will be constant as a well specified model will be covariance stationary and mean reverting.
a) it should be clear that this forecasting model is a time series model. other wise you can’t predict multiperiod.
b) to predict multiperiod model there is uncertainty. the process of predicting multiperiods advance in time-series is by chaining.
c) the first prediction which is for t+1 adds a bit of uncertaining e.
d) as you chain more and more you add more and more uncertainty. hence the variance of hte final multiperiod forecast (let’s say 10th period) is much higher than what you’d get by just predicting one period ahead.
The explanation makes sense when you explicilty talk about forecasts , and nothing else. If you claim a model is well specified, the variance of the error terms must be constant, the model will be mean reverting, and the model will be covariance stationary. If any of those assumptions are violated, why are you using the model to begin with? So all three choices are correct in their own way. I’m sure the chances of such crap appearing in the CFAI text is very low. Unless you (or whoever came up with the question) have a better explanation…
I’m not. However, the very first segment of the question says, “If the forecasting model is well specified…”
Choice B on its own would be correct. However, all I’m saying is that you can’t say B is right when the other two options are also correct. Can you give your reasons for why A or C would be incorrect? Especially within the context of the question.
If you go out 20 periods using a time series, the series will mean revert. You also assume that the variance will be constant. Anything wrong with these assertions?