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Empirical likelihood method has been applied to short-memory time seriesmodels by Monti (1997) through the Whittle's estimation method. Yau (2012)extended this idea to long-memory time series models. Asymptotic distributionsof the empirical likelihood ratio statistic for short and long-memory timeseries have been derived to construct confidence regions for the correspondingmodel parameters. However, computing profile empirical likelihood functioninvolving constrained maximization does not always have a solution which leadsto several drawbacks. In this paper, we propose an adjusted empiricallikelihood procedure to modify the one proposed by Yau (2012) forautoregressive fractionally integrated moving average (ARFIMA) model. Itguarantees the existence of a solution to the required maximization problem aswell as maintains same asymptotic properties obtained by Yau (2012).Simulations have been carried out to illustrate that the adjusted empiricallikelihood method for different long-time series models provides betterconfidence regions and coverage probabilities than the unadjusted ones,especially for small sample sizes.

Adjusted Empirical Likelihood for Long-memory Time Series Models