Multifractal regime detecting method for financial time series. (English) Zbl 1351.62182
Summary: We focus on time varying multifractality in time series and introduce a multifractal regime detecting method (MRDM) adopting a nonparametric statistical test for multifractality based on generalized Hurst exponent (GHE). MRDM is a practical method to discriminate multifractal regimes in a time series of any length using a moving time window approach with the adjustable time window size and the moving interval. MRDM is applied to simulations consisting of both multifractal and monofractal regimes, and the results confirm its validity. Using MRDM, we identify multifractal regimes in the time series of Korea composite stock price index (KOSPI) from 1990 through 2012 and observe the distinct stylized facts of the KOSPI return values in multifractal regimes such as the heavy tail distribution, high kurtosis, and the long memory in volatility. Surrogate tests based on improved amplitude adjusted Fourier transformation (IAAFT) algorithm, normal distribution, and generalized Student \(t\) distribution are performed for the validation of MDRM, and the probable causes of multifractality in the KOSPI series are discussed.
MSC:
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 62M02 | Markov processes: hypothesis testing |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 91G80 | Financial applications of other theories |
| 28A80 | Fractals |
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