engleski

Renyi functions for multifractal products of stationary processes and detecting multifractality under heavy-tailed effects

We provide rigorous proof that estimating the scaling function using the partition function can lead to nonlinear estimates under the presence of heavy tails. These results shed new light on many data sets that were claimed to be multifractal by using the partition function method. This is particularly important for financial data, which is generally accepted to possess heavy tails, thus can produce nonlinear scaling functions when there is no multiscaling. Scaling functions can be estimated correctly, but only when the range of finite moments is known. This makes multifractal definition based on moment scaling impractical. Results proved in the paper are concerned with processes with short range dependence properties. However, it is to expect that infinite moments produce similar behavior of the scaling function also in the case of long range dependence, with possible involvement of dependence parameter. It is known that processes such as multiplicative cascade and multifractal random walk have heavy-tails. It can thus be suspected that combined effect of dependence and heavy tails may produce nonlinear empirical scaling functions in these models.

Renyi functions; multifractality; heavy tails; multifractal spectrum

nije evidentirano