Abstract
Making predictions on the dynamics of time series of a system is a very interesting topic. A fundamental prerequisite of this work is to evaluate the predictability of the system over a wide range of time. In this paper, we propose an information-theoretic tool, multiscale entropy difference (MED), to evaluate the predictability of nonlinear financial time series on multiple time scales. We discuss the predictability of the isolated system and open systems, respectively. Evidence from the analysis of the logistic map, Hénon map, and the Lorenz system manifests that the MED method is accurate, robust, and has a wide range of applications. We apply the new method to five-minute high-frequency data and the daily data of Chinese stock markets. Results show that the logarithmic change of stock price (logarithmic return) has a lower possibility of being predicted than the volatility. The logarithmic change of trading volume contributes significantly to the prediction of the logarithmic change of stock price on multiple time scales. The daily data are found to have a larger possibility of being predicted than the five-minute high-frequency data. This indicates that the arbitrage opportunity exists in the Chinese stock markets, which thus cannot be approximated by the effective market hypothesis (EMH).
Highlights
Making predictions on the dynamics of time series of a system is a very interesting topic
We introduced a new information-theoretic tool of multiscale entropy difference (MED) to evaluate the degree of predictability for financial time series
The MED quantifies the contributions of the past values by reducing the uncertainty of the forthcoming values in time series on multiple time scales
Summary
Making predictions on the dynamics of time series of a system is a very interesting topic. For an isolated system, which does not exchange information with other systems, the predictability of the output time series is only determined by the degree of memory from the past values In such a case, the time series in unpredictable if it is purely random, like Gaussian white noise; whereas, information can be extracted for prediction by analyzing the temporal structure of a time series with memory. This paper contributes to evaluating the multiscale predictability of financial time series Another piece of evidence of this consideration is that the multiscale complexity (a tool of time series analysis that is associated with factors of the degree of memory, the temporal structure, and auto-correlations) have been measured [6,7], and the predictability of time series, which is closely related to those factors, can be analyzed on multiple time scales as well.
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