ABSTRACT

Stochastic processes may be used to model the behavior of an observed time series in a purely statistical way, without a direct physical interpretation of the parameters. For instance, may use a parametric model, which is characterized by a parameter vector T, to predict observations or to obtain a confidence interval for the mean. In some statistical applications, the observed time series is an aggregate of many individual time series. For instance, many economic data sets are generated in this way. An introduction to the role of long memory in the context of critical phenomena in physics is given in M. Cassandro and G. Jona-Lasinio. In an inter laboratory standardization experiment, D. R. Cox and M. W. H. Townsend considered the coefficient of variation of mass per unit length of worsted yarn. Cox proposed a physical explanation for these correlations, by constructing a model with hierarchical variation.