Quantifying the Multiscale Predictability of Financial Time Series by an Information-Theoretic Approach

Area of Science:

• Complex Systems Analysis
• Financial Econometrics
• Information Theory

Background:

• Evaluating the predictability of complex systems is crucial for understanding their dynamics.
• Assessing predictability across multiple time scales is essential for time series analysis.

Purpose of the Study:

• To introduce a novel information-theoretic tool, multiscale entropy difference (MED), for assessing the predictability of nonlinear financial time series.
• To analyze the predictability of isolated and open systems using the MED method.

Main Methods:

• Development and application of the multiscale entropy difference (MED) method.
• Analysis of nonlinear systems (logistic map, Hénon map, Lorenz system) for method validation.
• Application of MED to Chinese stock market data (five-minute and daily frequencies).

Main Results:

• The MED method demonstrates accuracy and robustness across various nonlinear systems.
• In Chinese stock markets, logarithmic returns are less predictable than volatility.
• Trading volume significantly aids in predicting stock price changes across multiple time scales.
• Daily stock market data exhibit higher predictability than five-minute high-frequency data.

Conclusions:

• The MED tool is effective for evaluating the predictability of financial time series.
• Findings suggest inefficiencies in Chinese stock markets, challenging the efficient market hypothesis (EMH).
• The study highlights the potential for arbitrage opportunities due to varying predictability levels.