Investigating the exchange rate between Japanese Yen and the Deutschmark: Arbitrage opportunities and a case for asymmetry

Deviations from the triangular equality are observed on foreign exchange (FX) markets when the respective rates are sampled at very high frequencies. Within the framework of nonstationary but cointegrated time series the triangular equation may be regarded as a long-run equilibrium. A time invariant and symmetric vector error correction model seems appropriate to explain the evolution of FX-returns depending on recent returns and on lagged deviations from the triangular equality. High frequency FX-rates are typically unequally spaced. Kalman recursions cope with the issue of missing values making (Quasi-) Maximum-Likelihood estimation feasible. The in-sample and out-of-sample forecasting performance of the common vector error correction model is compared to that of alternative specifications including a moving average process, periodic autoregressions, and asymmetric generalizations of the symmetric vector autoregression. For the actual JPY/DEM-rate the employed asymmetric time series models yield superior forecasting results compared to the remaining empirical models. Time dependent processes allowing for intra-day seasonality provide only minor improvements compared to time invariant models of corresponding autoregressive order.