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Scaling Behavior of Time Series and an Empirical Indication to Financial Prediction

Scaling exponent is used widely to measure the long-rang correlation of time series. The most typical original methods are Re-scale Range Analysis (R/S) and Detrended Fluctuation Analysis (DFA), both of which aim to calculate an effective exponent to characterize the given time series, but the latter is more effective to non-stationary series. In this paper, we firstly compare some typical series and find that when Hurst exponents are greater than 0.9, DFA is a better method to distinguish the two series with exponents of small difference in that range where non-stationary most likely exists. This is useful in solving the important open problem of telling whether the real financial data are Brownian motions. Furthermore, we reset the empirical series from stock market according to different time interval and employ the Binary Logistic Regression to estimate the prediction degree of the reset series with different exponents. Results prove that the model's predicting accuracy is significant when scaling exponent is beyond ± 0.1 deviation from 0.5, especially far less than 0.4 with non-stationary trait in raw series, showing the condition when predicting models should be introduced.