In this paper we apply the parametric approach to testing for dual long memory in daily exchange rate returns (first differences of daily log exchange rates) of twelve currencies against USD (4310 observations). The tests are based on ARFIMA-FIGARCH, HYGARCH and FIAPARCH models which are estimated by maximum likelihood method under the assumption of t-distribution, generalized error distribution and skewed t-distribution of innovation process. The results show presence of long memory in volatility of all twelve exchange rates and dual long memory in the returns of BRL/USD only. The HYGARCH model is found to be an appropriate volatility model with long memory for BRL/USD, NOK/USD and ZAR/USD. According to estimated FIAPARCH models there is an asymmetric response of volatility of BRL/USD, MXN/USD, NZD/USD and ZAR/USD to positive and negative shocks along with long memory.

ARFIMA, FIGARCH, HYGARCH, long memory, exchange rates

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