Abstract

We use a Monte-Carlo approach to investigate the performance of five different time-series estimators of the exponent ff in 1=f ff noise. We find that a maximumlikelihood estimator is markedly superior to Fourier regression methods and Hurst exponent methods. The results indicate that useful estimates of ff can be made from time series that are much shorter than generally presumed. PACS codes: 72:70:+m, 73:50:Td, 74:40:+k Keywords: noise, noise parameter estimation, noise generation 1 Introduction Long-term correlations have been observed in many types of time series from physical, biological, physiological, economic, technological and sociological systems. Examples include geophysical data [1, 2, 3] such as rainfall, temperature measurements, sun-spot numbers, earthquake frequencies, and river flows, frequency fluctuations in electrical oscillators [4], rate of traffic flow [1], voltage or current fluctuations in metal films and semiconductor devices [4], loudness fluctuations i...

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