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

Abstract

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.

Acknowledgements

We thank Mohamed Boutahar and Claude Deniau for their useful comments.

Notes

 If

then the series exhibits long-range dependence, while

suggests that it has a short memory.

 Note that

, and g(T) = T ^α, where 0 < α < 1. The regression range g(T) < T/2 is often used and there is not easily applicable rule for choosing g(T). Note that the most common choice for g(T) is T ^0.5 which may not be the best choice and may give biased results.