Spectral Analysis of Long Memory in Financial Volatility Dynamics: Evidence from the CAC 40 Stock Market Index
Keywords:
Spectral analysis, Volatility modeling, Long memory, CAC 40 indexAbstract
Long-memory processes are widely used in time series analysis to characterize persistent dependence structures over time. In financial markets, this phenomenon is particularly relevant for modeling volatility dynamics, which measure the variability and risk of asset returns. This study investigates the presence of long-memory behavior in financial volatility using a spectral analysis approach. While the persistence of volatility is a well-documented stylized fact in financial econometrics, traditional time-domain models such as ARCH, GARCH, and their extensions primarily capture short- and medium-term dependence in conditional variance, often failing to fully account for long-range dependence. This paper addresses this gap by employing a frequency-domain approach based on spectral analysis to detect long memory in volatility dynamics. The empirical study is conducted using daily data from the CAC 40 stock market index. The price series is transformed into logarithmic returns, with volatility proxied by squared returns. A comparative analysis between returns and squared returns reveals that returns exhibit weak autocorrelation, whereas squared returns display strong persistence—consistent with established stylized facts. To further examine this persistence, we perform spectral density analysis and a simulation study. The results reveal a significant concentration of spectral power at low frequencies, providing strong evidence of long-memory dynamics in volatility. These findings have important implications for volatility forecasting, risk management, and the specification of econometric models in financial applications.
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