Consider the statndard decomposition model $Y_t={}_t+S_t+x_t$ where ${}_t$ is a random

walk trend and $S_t$ is a seasonal series that can removed by the seasonal difference

opearator $U(B)=1+B+$cdots$+B^{d-1}$ where $d$ is the seasonal period and an even number.

Also $x_t$ is a stationary time series. Show that the operator $C(B)=B^{-\frac{d}{2}}\frac{1+B}{2d}$

removes the trend. Write an algorithm to multiply obain the coefficients of a polynomial

which is the product of two given polynomials and hence compute the filter coefficients

for the difference opearator $C(B)U(B).$