Integrated approach to the assessment of long range correlation in time series data

To assess whether a given time series can be modeled by a stochastic process possessing long range correlation, one usually applies one of two types of analysis methods: the spectral method and the random walk analysis. The first objective of this work is to show that each one of these methods used alone can be susceptible to producing false results. We thus advocate an integrated approach which requires the use of both methods in a consistent fashion. We provide the theoretical foundation of this approach and illustrate the main ideas using examples. The second objective relates to the observation of long range anticorrelation (Hurst exponent H