A DLM has the forecast function de ned over k = 01 current time t by ft(k) = at1 + at2k + at3rk cos(2 k +ct)

for some positive wavelength and some positive number r < 1, and where the quantities at1 at2 at3 ct are constants known at time t. Give real-valued and constant observation vector F and state evolution matrix Gof two di erent DLMs with this forecast function.