Modeling Risk Premia in Forward Foreign Exchange Rates as Unobserved Components: The Model Identification Problem

Is an autoregressive moving average model for the unobserved forward risk premium component always identifiable? Is the signal extraction-based approach always feasible? In this paper, we point out a theoretical framework to shed the light on the statistical problem of model identification. We find out that whenever a model for the unobservable forward risk premium is unidentifiable, we identify a new class of functions that we call: the noise generating functions (Hereafter NGF). These functions circumvent the model identification problem and help us make insights on the noise variances. We demonstrate that a model for the risk premium in the forward exchange rate is not always identifiable and the signal extraction methodology is not always feasible. In addition, our theoretical statements are applied to the empirically evidenced models within the related literature.