Long-Memory Modeling and Forecasting: Evidence from the U.S. Historical Series of Inflation

We report the results of applying semi-parametric long-memory estimators to the historical monthly series of U.S. inflation, and analyze their empirical forecasting performance over 1, 6, 12, and 24 months using in-sample and out-of-sample procedures. For comparison purposes, we also apply two parametric estimators, the naive AR(1) and the ARFIMA(1, d, 1) models. We evaluate the forecasting accuracy of the competing methods using the mean square error (MSE) and mean absolute error (MAE) criteria. We evaluate the statistical significance of forecasting accuracy of competing forecasts using the Diebold-Mariano (1995) test. Overall, our results preforms slightly better than the Lahiani and Scaillet (2009) threshold estimator based on the MSE and MAE criteria. This improvement in performance does not prove significant enough to cause a rejection of the null hypothesis of equality of predictive accuracy. The Boubaker (2017) estimator, on the other hand, significantly outperforms the time-invariant estimators over longer horizons. Over shorter horizons, however, the Boubaker (2017) estimator does not exhibit a significantly better predictive performance than the time-invariant long-memory estimators with the exception of the naive AR(1) model.