Efficient Estimation of Seasonal Long-Range-Dependent Processes

This paper studies asymptotic properties of the exact maximum likelihood estimates (MLE) for a general class of Gaussian seasonal long-range-dependent processes. This class includes the commonly used Gegenbauer and seasonal autoregressive fractionally integrated moving average processes. By means of an approximation of the spectral density, the exact MLE of this class are shown to be consistent, asymptotically normal and efficient. Finite sample performance of these estimates is examined by Monte Carlo simulations and it is shown that the estimates behave very well even for moderate sample sizes. The estimation methodology is illustrated by a real-life Internet traffic example. Copyright 2005 Blackwell Publishing Ltd.