Real exchange rate in the long run: A multi-resolution analysis

Findings from previous studies indicate that the long-run stationarity of the real exchange rate in different time horizons remains unclear. In order to shed light on this problem, we have adopted a new method which is widely used to analyze signals, the so-called wavelet transformation. This paper uses monthly data of the consumer price indices (CPI) and nominal exchange rates for six ASEAN countries for the 1998–2019 period. The unobserved component method is used to remove the seasonality and cyclicity of the CPI. Then, the real exchange rates are calculated. We use the unit root tests and wavelet transformation to verify if the purchasing power parity (PPP) holds in the long run in different time horizons. Key findings from the paper are as follows. First, the mean-reverting pattern of real exchange rate recurs itself for the period longer than 5 years. Second, the variation around trend using wavelet methodology can be used as a reliable indicator for future movements of the real exchange rate. Third, the high volatility of the exchange rate in the short run may be induced by arbitrage activities. Implications have emerged based on these findings for policymakers and investors in relation to the behaviour of the real exchange rate.