Four independent statistical calculations have been used to analyse average age time series ,
*In particular we are interested in calculatingi [1], [2], [8], [11] the Hurst parameter [6], which is a measure of the degree to which a time series is self-similar. One calculation is based on a property called the rescaled adjusted range statistic.
Details of this calculation are to be presented in a forthcoming publication. Results are discussed below.
*Periodogram analysis One of the characteristics of a self-similar time series is that the logarithm of its spectral density is dependent on the Hurst parameter and the logarithm of the frequency. Again, details will be presented elsewhere.
*Standard deviation of aggregates For a given k , the k -aggregated series is calculated. The standard deviation of this series is then found. As stated in [1] and [2] , the asymptotic slope of a logarithmic plot of the standard deviation vs the aggregation is a measure of the Hurst parameter.
*Autocorrelation function
The autocorrelation function of the time series has also been calculated. Although the calculation does not lead to an estimate for the Hurst parameter,, the autocorrelation function displays behaviour characteristic of self-similar processes, for large k.