Analysis And Forecast Of Financial Volatility Based On Symbolic Time Series Analysis

Financial high-frequency data include more market information and it is animportant part in the empirical research of market microstructure, this recognition hasspurred an extensive and vibrant research into it. The study of high-frequencyfinancial volatility is an important task in financial markets, especially in relation toasset allocation, risk management, security valuation, the pricing of derivatives andmonetary policy-making. The traditional methods almost focus on the specific dataand try to construct precise models, however, this article analyzes and forecasts theentire patterns of high-frequency financial data from a different angle.First，A new method of combining symbolic time series analysis and K-NearestNeighbors (K-NN) algorithm is put forward to forecast high frequency financialvolatility based on symbolic time series histogram. The original time series istransformed into symbolic time series and the histogram of symbolic series is used torepresent its overall distribution. The concept of symbolic histogram time series isintroduced and the K-NN algorithm is used to get the next period forecasting result ofsymbolic series histogram. In the K-NN algorithm, the Euclidean norm, χ2statisticsand the relative entropy are proposed to be the measurement of similarity between twosymbolic histogram time series according to the characteristics of symbolic serieshistogram. The geometrical property of the system itself is used to determine theembedding dimension of the symbolic histogram series. Second, the realized volatilitywhich can effectively exploit the information in intraday return data is applied tomeasure high-frequency intraday financial volatility, then permutation entropymethods are firstly introduced to analyze the ordinal structure of realized volatilityseries and generalized synchronization between two series. Besides, we use the totalprobability theorem to forecast the next day volatility level after knowing the orderpatterns of history realized volatility.The ability and effectiveness of the methods proposed in this article are tested byShanghai Composite Index or Shenzhen Component Index high frequency data whosesample period is5minutes. The results of histogram distribution forecasting indicatethat the forecasting errors are all acceptable. The forecasting distributions have thesame mean and smaller variance compared with the real distributions. While permutation entropy methods are used to analyze these two series, the dominatingorder patterns are determined and we find these two index’s realized volatility serieshave quite low generalized synchronization. Moreover, we forecast the next dayvolatility level based on principal order patterns and our forecasting results indicatethat the conditional order patterns of the main order patterns are still dominant.