ABSTRACT
P. Whittle's approximate maximum likelihood estimator requires the calculation of n integrals for each trial value of θ. This can be a time consuming task, in particular for large sample sizes and if θ has a high dimension. It should be noted, however, that the spectral density characterizes a process fully only if the process is Gaussian. While this might be the case in good approximation for the Nile River data, the Ethernet data are clearly non-Gaussian. This approximation was suggested by H. P. Graf for fractional Gaussian noise. He derived it in a different way, by assuming that periodogram ordinates at distinct Fourier frequencies are approximately independent exponential random variables with expected value equal to the spectral density.
