Inflation, Forecast Intervals and Long Memory Regression Models

We examine recursive out-of-sample forecasting of monthly postwar U.S. core inflation and log price levels. We use the autoregressive fractionally integrated moving average model with explanatory variables (ARFIMAX). Our analysis suggests a significant explanatory power of leading indicators associated with macroeconomic activity and monetary conditions for forecasting horizons up to two years. Even after correcting for the effect of explanatory variables, there is conclusive evidence of both fractional integration and structural breaks in the mean and variance of inflation in the 1970s and 1980s and we incorporate these breaks in the forecasting model for the 1980s and 1990s. We compare the results of the fractionally integrated ARFIMA(0,d,0) model with those for ARIMA(1,d,1) models with fixed order of d=0 and d=1 for inflation. Comparing mean squared forecast errors, we find that the ARMA(1,1) model performs worse than the other models over our evaluation period 1984-1999. The ARIMA(1,1,1) model provides the best forecasts, but its multi-step forecast intervals are too large.