Cycles and long-range behaviour in the European stock markets

This paper uses a modelling framework which includes two singularities (or poles) in the spectral density function, one corresponding to the long-run (zero) frequency and the other to the cyclical (nonzero) frequency. The adopted specification is very general, since it allows for fractional integration with stochastic patterns at the zero and cyclical frequencies and includes both long-memory and short-memory components. The cyclical patterns are modelled using Gegenbauer processes. This model is estimated using monthly data for five European stock market indices (DAX30, FTSE100, CAC40, FTSE MIB40, IBEX35) from January 2009 to January 2019. The results indicate that the series are highly persistent at the long-run frequency, but they are not supportive of the existence of cyclical stochastic structures in the European financial markets. The only clear evidence of a stochastic cycle is obtained in the case of France under the assumption of white noise disturbances; in all other cases, there is no evidence of cycles.