Inference and Forecasting for Fractional Autoregressive Integrated Moving Average Models, with an application to US and UK inflation

We discuss computational aspects of likelihood-based specification, estimation,inference, and forecasting of possibly nonstationary series with long memory. We use the \\ARFIMA$(p,d,q)$ model with deterministic regressors and we compare sampling characteristics of approximate and exact first-order asymptotic methods. We extend the analysis using a higher-order asymptotic method, suggested by \\cite{CoxRe.87}. Efficient computation and simulation allow us to apply parametric bootstrap inference as well. We investigate the relevance of the differences between the methods for the time-series analysis of monthly core consumer price inflation in the US and quarterly overall consumer price inflation in the UK. We concentrate on (stationarity) tests for the order of integration and on inference for out-of-sample forecasts of the price level.