Attractor misspecification and threshold estimation bias

Three regime threshold autoregressive models such as the BAND-TAR and EQ-TAR (Balke & Fomby, 1997) are commonly used when studying arbitrage in the presence of trade frictions because the estimated thresholds represent the size of the impediments to arbitrage. This paper shows that, while commonly overlooked, the attractors in these models play an important role in threshold estimation. In particular, misspecified attractors cause systematic biases in estimated thresholds. This paper proposes a generalized three regime TAR model that nests both the BAND-TAR and the EQ-TAR models and allows the attractor to be freely estimated. Simulations suggest that the generalized model mitigates the biases that arise when the attractor is misspecified.