The purpose of this paper is to address the issue of the forward premium anomaly by using two different approaches: the long memory process and Multivariate GARCH. Initially, through the ARFIMA model, we study the properties of the forward premium on foreign exchange markets, including the presence of any long memory. Since the univariate study framework obscures the effect of conditional covariances in the measurement of risk, the transition to a more parsimonious multivariate framework is required. Therefore, we estimate, in a second time, the DCC-MVGARCH model to capture the dynamic links between forward premium series and the spot exchange return. The estimation results argue in favor of a forward premium that exhibits a phenomenon of long memory. In addition, they reveal the existence of a significant correlation sensitivity to shocks following a process of mean reversion and the detection of a strong correlation between these forward premiums and low correlation between the forward premium and the spot exchange return.
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