Financial Volatility Pattern Recognition And Outliers Detection Based On Wavelet Analysis

Financial volatility is an inherent feature of all financial markets, which plays animportant role in portfolio allocation, the pricing of financial products, financial riskmanagement and other financial areas. Especially, the study of financial volatilitypattern recognition and the related anomaly detection is significant to investors andregulators. In practice, the features of financial volatility are generally got form returnseries of financial assets. This article studies the problems of financial volatilitypattern recognition and financial return time series outliers detection though newmethods which are the combination of wavelet analysis and symbolic time seriesanalysis, D-Markov model, financial volatility models.First, a new method of combining wavelet analysis, symbolic time series analysisand D-Markov model is proposed to identify the financial volatility pattern and detectabnormal pattern. Wavelet coefficient sequence is generated from the discrete wavelettransform of volatility series. Then, the D-Markov model of symbolic time series,which is the wavelet coefficient sequence after symbolization, is build to calculate thestate probability vector and anomaly measure between volatility vectors.Subsequently, the anomaly measure is used to identify the financial volatility patternand detect abnormal pattern. Second, a wavelet-based method of outliers detectionand location is put forward to analyze financial return time series. The residuals seriescan be got after portraying financial return time series by using volatility models. Thewavelet coefficients series which could be got through discrete wavelet transform areanalyzed. The location of the maximum value which also is greater than the thresholdgot from Monte Carlo simulation in wavelet coefficients series is marked and placedin a position set. Then, the wavelet coefficients series is rebuilt by setting the value ofabove position to zero and a new residuals series can be got though inverse discretewavelet transform. Reusing the above steps until the maximum value of waveletcoefficients series is not greater than the threshold. The outliers is detected andlocated by the position set.The feasibility and validity of the methods proposed in this article are tested byShanghai Composite Index or Shenzhen Component Index data. The volatility patternwhich is similar to the selected standard volatility pattern can be found and the abnormal pattern can be identified. Meanwhile, a wavelet-based method of outliersdetection and location is implemented to analyze these two series, the outliers in bothseries are detected effectively and located accurately.