Fit a trend $\widehat T_t$, form $D_t=X_t-\widehat T_t$, and estimate the period-25 seasonal effect by
$$
\widehat S_j=\frac1M\sum_{r=0}^{M-1}D_{j+25r},
\qquad j=1,\ldots,25.
$$
The residual is $R_t=X_t-\widehat T_t-\widehat S_{t\bmod25}$. This additive decomposition is sensible when seasonal amplitude does not systematically change with the level or trend; multiplicative seasonality would require a logarithmic transform or ratio decomposition.


Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-218/6/b/solution