Can a Lucas model with habit generate realistic conditional volatility in exchange rate returns?

In this paper, we attempt to give a theoretical underpinning to the well established empirical stylized fact that asset returns in general and the spot FOREX returns in particular display predictable volatility characteristics. Adopting Moore and Roche's habit persistence version of Lucas model we find that both the innovation in the spot FOREX return and the FOREX return itself follow 'ARCH' style processes. Using the impulse response functions (IRFs) we show that the baseline simulation FOREX series has 'ARCH' properties in the quarterly frequency that match well the 'ARCH' properties of the empirical monthly estimations in that when we scale the x-axis to synchronize the monthly and quarterly responses we find similar impulse responses to one unit shock in variance. The IRFs for the ARCH processes we estimate 'look the same' with an approximately monotonic decreasing fashion. The Lucas two-country monetary model with habit can generate realistic conditional volatility in spot FOREX return.