On testing and forecasting in fractionally integrated time series models

Abstract: This volume contains five essays in the field of time series econometrics. All five discuss properties of fractionally integrated processes and models. The first essay, entitled Do Long-Memory Models have Long Memory?, demonstrates that fractional integration can enhance the memory of ARMA processes enormously. This is however not true for all combinations of diffe-rencing, autoregressive and moving average parameters. The second essay, with the title On the Effects of Imposing or Ignoring Long-Memory when Forecasting, investigates how the choice between mo-delling stationary time series as ARMA or ARFIMA processes affect the accu-racy of forecasts. The results suggest that ignoring long-memory is worse than imposing it and that the maximum likelihood estimator for the ARFIMA model is to prefer. The third essay, Power and Bias of Likelihood Based Inference in the Cointegration Model under Fractional Cointegration, investigates the performance of the usual cointegration approach when the processes are fractionally cointegrated. Under these circumstances, it is shown that the maximum likelihood estimates of the long-run relationship are severely biased. The fourth and fifth essay, entitled respectively Bootstrap Testing for Fractional Integration andRobust Testing for Fractional Integration using the Bootstrap, propose and investigate the performance of some bootstrap testing procedures for fractional integration. The results suggest that the empirical size of a bootstrap test is (almost) always close to the nominal, and that a well-designed bootstrap test is quite robust to deviations from standard assumptions.