The consequences of seasonal adjustment for periodic autoregressive processes



Summary  This paper examines the effect of X-11 seasonal adjustment on periodic autoregressive processes, using both analytic techniques and simulation. Analytical results show that adjustment reduces (but does not eliminate) periodicity in the coefficients of a stationary PAR(1) process, and it generally moves the coefficients towards unity. A nonstationary periodically integrated process is converted into a process with a conventional unit root and induced periodic heteroscedasticity. Simulations confirm that, for finite samples, evidence of periodicity in the coefficients and in residual heteroscedasticity may remain after adjustment, but periodic variation in long-run coefficients is annihilated. The overall conclusion is that adjustment alters, but does not destroy, periodic properties.