Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 218 / 6 / c / Solution

A period-50 business cycle can be a stochastic cycle in the residual process and need not violate additive trend-plus-period-25 seasonality. Applying $1-B^{50}$ discards the first 50 of only 100 observations and introduces a noninvertible seasonal moving-average factor, creating strong artificial dependence and risking overdifferencing rather than modeling the cycle.