Long-memory and shifts in the unconditional variance in the exchange rate euro/US dollar returns

In this paper two characteristics a priori contradictory and yet coexistent in the daily returns of exchange rate euro/US dollar are drawn. The non-stationarity of the covariance structure of the series is shown and, after the extraction of the unstable variance using the algorithm based on the cumulative sums of squares of Inclan and Tiao (Journal of the American Statistical Association, 1994, 89(427), 913-23), the existence of long-memory in the filtered series. Does the non-stationarity of the unconditional variance explain the phenomenon of long-memory? Thus a classic debate is found of which the exit does not again elucidate.