This paper deals with the analysis of the SOI and EQSOI series and their statistical properties, focussing in particular in their cyclical pattern and its persistence across time. For this purpose, we use a long memory model that is characterized because the spectral density function is unbounded at a frequency away from zero. Our results indicate that the two series display a long memory pattern, with the order of integration in the interval (0, 0.5) and the length of the cycles ranging between three and four years.JEL Classification: C00; C02; C22; Q54;