Mandelbrot Peters Peters 1 1 R /S R /S Resealed Range Analysis Hurst Hurst Hurst Mandelbrot 4 Hurst 8 Hurst 8 σ T 1 2 1

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1 4 1 5 Vol 41 No Journal of Shanghai Normal UniversityNatural Sciences Oct 运用了分形理论中的 R /S 分析法对中国的三大股市 ( 上证, 深证和香港的恒生指数 ) 以及欧美的三大股市 ( 道琼斯纳斯达克以及标普 500 指数 ) 的近 10 年 ( 2002 ~ 2011) 的股票指数作了差别研究我国股市的月对数收益率的 Hurst 指数为 0 74 左右 ; 而国外的则在 0 77 左右国内三大股市的平均循环周期在 600 d 左右, 而国外三大股市在 1150 d 左右道琼斯指数对上证指数价格变化影响较大 ; 恒生指数对深证指数的价格波动影响要比上证指数的价格波动影响大中外股指均具有比正态分布更高的峰度, 且在最初的一到两个周期内, 数据呈现右偏尖峰后尾的分布特征, 之后则呈现左偏尖峰后尾的分布特征而国外股指的数据分布更接近于正态分布本研究对股市研究者了解和借鉴近年来国外股市行情有着一定的指导意义有效市场理论 ; Hurst 指数 ; R /S 分析法 ; 波动性与相关性 ; 正态检验 F O 29 0 A R /S Hurst R

2 Mandelbrot Peters Peters 1 1 R /S R /S Resealed Range Analysis Hurst Hurst Hurst Mandelbrot 4 Hurst 8 Hurst 8 σ T T 1 Hurst R /S Hurst H 0 5 Peters R /S t u X t N = N X t N = t e n - M N n = 1 e n u M N N e n R = MaxX t N - MinX t N R X MaxX X MinX X Hurst Hurst R /S = N = a = H = Hurst X t N R /S = an H 2 H 0 5 H 0 5 H

3 σ T H 3 Hurst H = < H < < H < 1 H H H = Hurst Hurst 14 ( ) S t = ln p t p t - 1 p t t S t t 1 x t A N I a a = 1 2 N I a x t x k a k = 1 2 N I a X k a = k i = 1 x i a - x a k = 1 2 N x a I a x k a X k a I a x k a 2 I a R Ia R Ia 3 N R /S N = Max 1 k NX k a - Min 1 k NX k a R /S N = 1 R A A Ia /S Ia a = 1 4Hurst R /S N = an H 5 Hurst lnn Hurst ln R /S N = H lnn + H Ina ~ http/ /finance yahoo com / R /S

4 / / 1 /1 /2002 ~ 31 /12 / /1 /2002 ~ 31 /12 / /1 /2002 ~ 31 /12 / /1 /2002 ~ 31 /12 / /1 /2002 ~ 31 /12 / /1 /2002 ~ 31 /12 / R /S R /S 2 Hurst 0 5 Hurst Hurst R Hurst Hurst Hurst Hurst Hurst 16

5 R /S 2 Hurst Hurst Hurst Hurst Hurst Hurst Hurst 17 Hurst Hurst 18 Hurst V 17 Mandelbrot Crossover Point R /S lnr /S- lnn lnn * 0 5 < H < 1 H = 0 5 n *

6 5 459 Hurst V 20 V n = R /S n 7 槡 n V n lnn H > 0 5V n lnn H < 0 5V n lnn V n 20 V V n V n lnn d 3 V - V n 3 3 /d /d /d

8 5 461 SPSS Bivariate Correlation Pearson Pearson Correlation 4 4 Pearson Correlation SHANGHAI SZSE HANGSENG DOW Pearson Correlation SPSS 0 SPSS SPSS A % 0 1% B % C JB Jarque - Bera 22 OLS S S = x t - 珋 x 3 n σ 4 x K K = x t - 珋 x 4 n σ 4 x 8 9

9 Jarque Bera [ ] JB = n K - 6 S n S K JB 2 S = 0 K = 3 JB = 0 JB JB P P Jarque - Bera 1% JB ~ 2005 JB JB 02 /01 /02-31 /12 / /01 /04-31 /12 / /01 /06-31 /12 / /01 /08-31 /12 / /01 /10-31 /12 / /01 /02-31 /12 / /01 /04-31 /12 / /01 /06-31 /12 / /01 /08-31 /12 / /01 /10-31 /12 / /01 /02-31 /12 / /01 /04-31 /12 / /01 /06-31 /12 / /01 /08-31 /12 / /01 /10-31 /12 / /01 /02-31 /12 / /01 /04-31 /12 / /01 /06-31 /12 / /01 /08-31 /12 / /01 /10-31 /12 /

10 R /S Hurst Hurst Hurst 3 Hurst Hurst Hurst V n In n d d 23

11 J J J MANDELBROT B B The Fractal Geometry of NatureM New YorkW H Freeman and company MANDELBROT B The Variation of Certain Speculative PricesM COOTNER P The Random Character of Stock Market Prices CambridgeM I T Press PETERS E E Chaos and order in the capital marketsm New YorkJohn Wiley & Sons press HURST E H Long-term storage capacity of reservoirs J American Society of Civil Engineers PETERS E Fractal Market AnalysisApplying Chaos Theory to Investment and EconomicsM New YorkJohn Wiley & Sons Inc R / S J ADDISON P S Fractal and Chaos-An Illustrated Course M Bristol and PhiladelphiaInstitute of Physics Publishing Hurst J BO Qu ADDISON P S Development of FBMINC model for particle diffusion in fluidsj International Journal of Sediment Research J R /S J /OL http www paper edu cn 15 J Hurst D Hurst D D MANDELBROT B B Statistical methodology for nonperiodic cyclesfrom covariance to R /S analysisj Annals of

12 5 465 Economic and Social Meawrernent J SPSS M J J The fractal research on several large stock market in China and western country QU BoOU Rong-junHE HuiWANG XiangYAN Meng-ling School of Science Nantong University Nantong China AbstractThe R /S method of the fractal theory was used in analysis the most influential stock markets in China Shanghai Composite Index-SSEC the Shenzhen Composite Index-SZCI and Hang Seng Index-HSI in HongKongand the most impact foreign stock markets the Dow Jones the Nasdaq and the S&P 500in recent 10 years stock index to study their differences The Hurst exponent for the logarithmic rate of monthly return for Chinese stock markets were around 0 74 while the Hurst exponent for the western were around 0 77 The average cycle for Chinese stock markets were around 600 days while westerns were around 1150 days The price of the Dow Jones index had a greater influence on the price of SSEC than other markets and HSI had a greater influence on SSCI than SSEC Chinese and foreign markets had higher kurtosis than normal distribution and during the first one or two cycle the price data presented a right-skewed peak and fat-tailed distribution characteristics The data presented a left-skewed peak and fat-tailed distribution afterwards At the same time the foreign data is much closer to normal distribution This research is a good guidance for stock researcher understanding and studying the foreign stock markets Key wordsefficient market theoryhurst exponentr /S analysisvolatility and correlationnormality test ( 责任编辑 : 冯珍珍 )

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49 2 Vol 49 No 2 2016 3 Journal of Jiangxi Normal University Social Sciences Mar 2016 200042 341000 1936 1949 K262 9 A 1000-579 2016 02-0136 - 13 On the Salaries of Staffs in County Judicial Department