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Long-Range Dependence in Financial Markets: A Moving Average Cluster Entropy Approach
Pietro Murialdo1, Linda Ponta2, Anna Carbone1
1Institute of Condensed Matter Physics and Complex Systems, DISAT, Politecnico di Torino, 10129 Torino, Italy.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
Moving average cluster entropy reveals market horizon dependence in financial time series. This complexity is linked to long-range positive correlations, offering insights into price dynamics and risk analysis.
Area of Science:
- Quantitative Finance
- Economic Complexity
- Time Series Analysis
Background:
- Economic and social systems exhibit intangible complexity.
- Financial time series contain dynamical processes for information production, storage, and transmission.
- Market and horizon dependence are observed in high-frequency financial data.
Purpose of the Study:
- Investigate complexity in economic systems via financial time series.
- Analyze market and horizon dependence using moving average cluster entropy.
- Explore the relationship between cluster entropy and long-range correlated stochastic processes.
Main Methods:
- Applied the moving average cluster entropy approach to financial time series.
- Utilized Autoregressive Fractionally Integrated Moving Average (ARFIMA) and Fractional Brownian Motion (FBM) models.
- Generated extensive series with varying Hurst exponent (H) and ARFIMA parameters (p, d, q).
Main Results:
- A systematic relation was found between moving average cluster entropy and long-range correlation parameters (H, d).
- Horizon dependence of cluster entropy is linked to long-range positive correlation in financial markets.
- ARFIMA processes with specific differencing parameters (d ≈ 0.05, 0.15, 0.25) align with entropy results for DJIA, S&P500, and NASDAQ.
Conclusions:
- Financial market behavior exhibits variability in price returns, consistent with multi-temporal scale dynamics.
- The study identifies short- and long-run volatility components in price dynamics.
- The moving average cluster entropy approach effectively captures horizon dependence for risk analysis indices over short horizons (1-12 months).
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