پیش بینی نوسانات SSEC در بازار سهام چین با استفاده از تحلیل چند برخالی

In this paper, taking about 7 years’ high-frequency data of the Shanghai Stock Exchange Composite Index (SSEC) as an example, we propose a daily volatility measure based on the multifractal spectrum of the high-frequency price variability within a trading day. An ARFIMA model is used to depict the dynamics of this multifractal volatility (MFV) measures. The one-day ahead volatility forecasting performances of the MFV model and some other existing volatility models, such as the realized volatility model, stochastic volatility model and GARCH, are evaluated by the superior prediction ability (SPA) test. The empirical results show that under several loss functions, the MFV model obtains the best forecasting accuracy.

Modeling and forecasting volatility in financial markets is a key issue in many important fields, such as derivative products pricing, portfolio allocation and risk measurement. The seminal paper of Engle [1] has paved the way for the development of a large number of so-called historical volatility models in which a time varying volatility process is extracted from financial return data. Many of these models can be regarded as variants of the generalized autoregressive conditional heteroskedasticity (GARCH) models [2]. A rival class for ARCH is associated with the stochastic volatility (SV) models [3]. Both GARCH and SV models are regularly used for the analysis of daily, weekly and monthly returns. However the recent widespread availability of intraday high-frequency prices of financial assets and the work done on them have shed new light on the concept of volatility: as a matter of fact, data sampled at regular intradaily intervals can be summarized into a measure called realized volatility (RV) which, under some assumptions, is a consistent estimator of the quadratic variation of the underlying diffusion process [4]. In principle, the volatility measures derived from high-frequency data should prove to be more accurate, hence allowing for forecast efficiency gains. Nevertheless, recently Ref. [5] shows that realized volatility is prone to all sorts of microstructure problems. Since the suggestion of Mandelbrot [6] that multifractal is a powerful tool for depicting volatility complexities in financial markets, much research has been done in this field. However most of these studies focus on empirical tests of multifractality in different financial data sets. So we wonder whether multifractal analysis can contribute to the measurement and forecasting accuracy of volatility in financial markets. Taking high-frequency data of SSEC index in Chinese stock market as an example, first we propose a so-called multifractal volatility (MFV) measure based on the multifractal spectrum of high-frequency price movements within one trading day. Second similar to realized volatility, we also propose an ARFIMA process to model the dynamics of MFV and use a rolling-window method to forecast the volatility of SSEC one day ahead. Finally, we use a formal test for superior prediction ability (SPA) proposed by Ref. [7] to evaluate the forecasting performance of the MFV model and compare it to other popular volatility models, such as RV, SV and GARCH models. The empirical results show that under several loss functions, i.e., mean square error adjusted for heteroskedasticity (HMSE) and mean absolute error adjusted for heteroskedasticity (HMAE), the MFV model obtains the best forecasting accuracy. This paper is organized as follows. In the next section, we introduce the sample data and discuss how daily and intraday returns are constructed. In Section 3, we discuss how realized volatility is derived from intraday returns and the ARFIMA model for RV. In Section 4, we introduce the calculation of the multifractal volatility measure from the multifractal spectrum of high-frequency price movements within one trading day. In Section 5, the historical volatility models are briefly described. The out-of-sample forecasting methodology and SPA test are discussed in Section 6, and in Section 7, the estimation and forecasting results are presented. Section 8 summarizes the conclusions.

In this paper, taking about 7 years’ high-frequency data of Shanghai Stock Exchange Composite Index (SSEC) as an example, we propose a daily volatility measure based on multifractal spectrum of the high-frequency price variability within a trading day. An ARFIMA(1,d,1)(1,d,1) model is also constructed to depict the dynamics of the so-called multifractal volatility (MFV) measure. To testify the efficiency of the MFV measures, we compare the one-day ahead volatility forecasting performance of the MFV model with other three popular models, i.e., realized volatility model, SV and GARCH. The empirical results of the superior prediction ability (SPA) test show that the ARFIMA-lnMFV model outperforms all the other alternative models when the loss functions of HMSE and HMAE are taken into account. Furthermore, we find that volatility models based on high-frequency data, RV and MFV models, produce better volatility forecasts than those models based on daily data. These results suggest that the multifractal analysis of high-frequency data of financial assets may produce much valuable statistical information on volatilities and their dynamical characteristics. This information may help in the further research on derivative products pricing, portfolio allocation and financial risk management.