Large Sample Simulation of Flicker Noise

The computer simulation of complex systems often requires efficient recursive algo-rithms to generate various noise types. Flicker noise often occurs in frequency and time systems and long samples (a million or more lags) are needed. In June of 1971 two papers on flicker noise simulation were published independently. ~andelbrot [ ' l based the simulation on the sum of several low pass filtered white, Gaussian noises. He showed that the noise level and the filter passband of each noise can be selected to provide an approximate flicker noise over a finite but arbitrary spectral range. The precision of fit to the fiicker spectrum can be arbitrarily good depending on the number of independent elements used. Barnes and ~ a r v i s l ~ ] based their simulation on a cascade of lead-lag filters. Similarly, the extent and goodness of fit of the output noise depends only on the number of filter stages used. The Barnes-Jarvis procedure has an exact inverse which has advantages over the Mandelbrot method in some statistical applications other than noise simula-tion. The Barnes-Jarvis method can be expressed as an ARIMA model, but certai