Multifractal Early Warning Signals about Sudden Changes in the Stock Exchange States

Critical phenomena in stock exchange are regularly occurring and difficult to predict events, often leading to disastrous consequences. The presented paper is devoted to the search and research of early warning signals of critical transitions in stock exchange based on the results of a multifractal analysis of a series of transactions in shares of public companies. We have proposed and justified the use of certain features of behavior of multifractal spectrum shape parameters such as signals. As model time series, on which methods of multifractal analysis were tested, we used a series of the number of unstable sites of the sandpile automaton on the random Erdős–Rényi graph, self-organizing into critical and bistable states. It was found that the early warning signals for both cellular automata and stock exchanges are an increase in the magnitude of the maximum position, a decrease in the width, and a decrease, followed by a sharp increase, in the value of the spectrum asymmetry parameter.