Do Real Exchange Rates Follow a Random Walk?: Extracted Inflation-Based Evidence from Japanese Yen

Abstract

Using the pure price inflation rates extracted and estimated by an innovative financial-asset pricing method, we build and estimate univariate time series models of Japanese yen per U.S. dollar real exchange rates. Employing three methods of modeling, we find consistently that the extracted price index-based real exchange rate, r(t), obeys a stationary, mean-reverting process. The mean-reverting behavior detected is consistent with the less restrictive version of absolute purchasing power parity in which a real exchange rate is allowed to temporarily deviate from its mean. Further, the stationarity of r(t) is fundamentally attributable to frequent and sharp changes in expectations reflected in goods prices that are implied by the extracted pure price inflation rates. Finally, an intuitive conjecture is presented that, in the long run, stationary series (r(t)) would be less difficult to predict than nonstationary (random-walk) time series, because of the long-run, mean-reverting behavior of r(t). The conjecture is supported by the out-of-sample forecasting performance comparison between r(t) and the random-walk CPI-based real exchange rate, for three- to six-month forecast horizons. This would reinforce evidence of the stationarity of r(t). A desirable feature of stationary real exchange rate is also presented with regard to equilibrium error.