Self-similar characteristics of the currency exchange rate in an economy in transition

In this paper, we present an analysis of the self-similar characteristics of the temporal series describing the daily exchange rate of the Romanian currency unit “Leu” (ROL) with respect to the US Dollar (USD). The relevance of this investigation consists in the exchange rate being a proper indicator for the dynamics of an economy in transition from a command-type structure towards an open market one. The time series is exhibiting self-similar cells of dimensions obeying a definite power law scaling rule that is related to different categories of economic agents. By using a crossing-type analysis based on the Hurst exponent and the frequency spectrum, five categories were detected. A simple model based on active filters with prevailing feedforward loops working close to the unstable regime, each one describing an economic agent under the stress of a hostile economic environment, is proposed for the dynamics of the fragmentation–defragmentation process. The model qualitatively reproduces the self-similarity characteristics of the currency exchange rate of an economy in transition, subjected to deep structural changes. We observe that the “in-phase evolution” of the economic agents causes the statistical self-similarity to resemble a theoretical self-similarity.