This paper illustrates how to compare different agent-based models and how to compare an agent-based model with real data. As examples we investigate ARFIMA models, the probability density function, and the spectral density function. We illustrate the methodology in an analysis of the agent-based model developed by Levy, Levy, Solomon (2000), and confront it with the S&P 500 for a comparison wi...

Researchers in psychology are paying increasing attention to temporal correlations in performance on cognitive tasks. Recently, T. Thornton and D. L. Gilden (2005) introduced a spectral method for analysing psychological time series; in particular, this method is tailored to distinguish transient serial correlations from the persistent correlations characterised by 1/f noise. Thornton and Gilde...

The elevation of Great Salt Lake (GSL) has a great impact on the people of Utah. The flood of GSL in 1982 has caused a loss of millions of dollars. Therefore, it is very important to predict the GSL levels as precisely as possible. This paper points out the reason why conventional methods failed to describe adequately the rise and fall of the GSL levels – the long-range dependence (LRD) propert...

We study the autocorrelation structure and the spectral density function of aggregates from a discrete-time process. The underlying discrete-time process is assumed to be a stationary AutoRegressive Fractionally Integrated Moving-Average (ARFIMA) process, after suitable number of differencing if necessary. We derive closed-form expressions for the limiting autocorrelation function and the norma...