A simple filter often applied in empirical econometric work is the seasonal difference filter (1 − L s ), where s is the number of observations per year, typically s = 2, 4, 12 or 52. The seasonal differencing assumes that there are unit roots at all the seasonal frequencies. The seasonal difference filter can be written as the product of (1 − L) and the seasonal summation filter S( L), which for quarterly data is S( L) = (1 + L + L 2 + L 3). The quarterly seasonal summation filter has the real root − 1 and the two complex conjugate roots ± i.