Revisiting detrended fluctuation analysis

Half a century ago Hurst introduced Rescaled Range (R/S) Analysis to study fluctuations in time series. Thousands of works have investigated or applied the original methodology and similar techniques, with Detrended Fluctuation Analysis becoming preferred due to its purported ability to mitigate nonstationaries. We show Detrended Fluctuation Analysis introduces artifacts for nonlinear trends, in contrast to common expectation, and demonstrate that the empirically observed curvature induced is a serious finite-size effect which will always be present. Explicit detrending followed by measurement of the diffusional spread of a signals' associated random walk is preferable, a surprising conclusion given that Detrended Fluctuation Analysis was crafted specifically to replace this approach. The implications are simple yet sweeping: there is no compelling reason to apply Detrended Fluctuation Analysis as it 1) introduces uncontrolled bias; 2) is computationally more expensive than the unbiased estimator; and 3) cannot provide generic or useful protection against nonstationaries

Forecasting the real output using fractionally integrated techniques

The annual structure of the real GDP in the UK, France, Germany and Italy is examined by means of fractionally integrated techniques. Using a version of a testing procedure due to Robinson (Journal of the American Statistical Association, 84, 1420-37, 1994), it is shown that the series can be specified in terms of I(d ) statistical models with d higher than 1. Thus, the series are nonstationary and non-mean-reverting. The forecasting properties of the selected models for each country are also examined.