Exchange rate predictability: Multi-State Markov-Switching model and trend with controlled smoothness

Abstract This study presents an exchange rate (Mexican Pesos / U.S. Dollar) forecasting model. The statistical methodology used is based on the Multi-State Markov-Switching model with three different specifications. The model is applied to the trend of the time series data instead of the original observations to mitigate the effect of outliers and transitory blips. The filtering technique employed to estimate the trend allows us to control the amount of smoothness in the resulting trend. By doing this, the Markov-Switching approach captures the trend persistence of exchange rates more accurately and enhances both in-sample and out-of-sample forecast performance. Our results show that correctly identifying the trend in the exchange rate (Mexican Pesos / U.S. Dollar) plays a key role in achieving superior forecasting ability concerning the simple random walk. Besides the new approach for estimating a trend with controlled smoothness, we emphasize that when working with asset prices time series, a usual assumption is that the series behaves as a random walk, that is, as an I(1) process, and not as an I(2) process. Since we are interested in decomposing a financial time series into trend plus noise, we use the exponential smoothing (ES) filter rather than the Hodrick-Prescott (HP) filter, as other authors have done. Applying the HP filter to an I(1) process, as wrongly done, yields a specification error in the sense that a sub-optimal procedure is used.