Abstract

Multifractal analysis is widely used for characterizing financial signal behaviors and self-similarity. Different phenomena in financial markets, such as financial crises or periods of high volatility, lead to different scaling behaviors. However, there have been a few studies relating the relation between scaling behaviors and regime switching in a financial market. With this motivation, this chapter demonstrates multifractal analysis and how it can be utilized to investigate the scaling behaviors of the return signals in different regimes of a financial market. We demonstrated the method in various indices of financial markets, including FCHI, DAX, HSI, KOSPI, NIKKEI, SET, NASDAQ, and NYSE. Using the hidden Markov model, the return signals are categorized into two regimes labeled as low volatility or high volatility. We discovered that the global Hölder exponents of both high-and low-volatility periods are less than 0.5, indicating that the signals tend to retain their antipersistent behaviors. Furthermore, multifractal structures behave differently in different regimes, such as long left tails are found in a high-volatility regime, but long right tails are found in a low-volatility regime, suggesting that multiscaling structures are sensitive to local fluctuation in different regimes. Through the empirical study of financial regimes and signal structures in terms of multiscaling, the relation between signal behaviors and market regimes can shed insights into the market status and provide indicators of regime switching that can influence traders' decisions.