Out-of-sample forecasting of foreign exchange rates: The band spectral regression and LASSO

We propose to utilize the band spectral regression for out-of-sample forecasts of exchange rates. When one period ahead forecast is considered, there is some evidence that the band spectral regression improves its accuracy, especially when the Taylor rule fundamentals model is employed. However, when the forecasting horizon increases, the purchasing power parity (PPP) fundamentals model is found to be powerful, and we can improve the out-of-sample forecast by selecting appropriate frequency bands. Bayesian model averaging shows that placing a large weight on the business cycle frequency improves the accuracy of the out-of-sample forecasting of the PPP model (as well as the monetary fundamentals model) when a longer forecasting horizon is our focus. Without specifying the frequency bands prior to applying the regression, LASSO can provide better out-of-sample exchange rate forecasts for many cases – most patently for the PPP fundamentals model – and provide information about the dynamic relationship between forecasting variables and exchange rates. The frequency domain approach not only improves the accuracy of exchange rate forecast but provides insights for understanding why the PPP fundamentals act as a powerful predictor when the forecasting horizon increases and there is a possible improvement in the time domain regression forecast.