Suppose the quarterly seasonal process {????????} is represented as ???????? = ???????? + ????2????, where

???????? follows a ‘‘seasonal random walk’’ model (1 − ????4)???????? = ????0 + ????1????, and ????1???? and

????2???? are independent white noise processes with variances ????2

????1 and ????2

????2

, respectively.

Show that ???????? follows the seasonal ARIMA model (1 − ????4)???????? = ????0 + (1 − Θ????4)????????, and determine expressions for Θ and ????2

???? in terms of the variance parameters of the other two processes. Discuss the implication if the resulting value of Θ is equal (or very close) to one, with regard to deterministic seasonal components.