Nonlinear behaviors of tail dependence and cross-correlation of financial time series model. (English) Zbl 1407.62382

Deng, Wei; Wang, Jun

Abstr. Appl. Anal. 2014, Article ID 965081, 13 p. (2014).

Summary: Nonlinear behaviors of tail dependence and cross-correlation of financial time series are reproduced and investigated by stochastic voter dynamic system. The voter process is a continuous-time Markov process and is one of the interacting dynamic systems. The tail dependence of return time series for pairs of Chinese stock markets and the proposed financial models is studied by copula analysis, in an attempt to detect and illustrate the existence of relevant correlation relationships. Further, the multifractality of cross-correlations for return series is studied by multifractal detrended cross-correlation analysis, which indicates the analogous cross-correlations and some fractal characters for both actual data and simulative data and provides an intuitive evidence for market inefficiency.

MSC:

62P05	Applications of statistics to actuarial sciences and financial mathematics
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H05	Characterization and structure theory for multivariate probability distributions; copulas
62G32	Statistics of extreme values; tail inference
91G99	Actuarial science and mathematical finance
28A80	Fractals

References:

[1]	Gopikrishnan, P.; Plerou, V.; Amaral, L. A. N.; Meyer, M.; Stanley, H. E., Scaling of the distribution of fluctuations of financial market indices, Physical Review E, 60, 5, 5305-5316 (1999) · doi:10.1103/PhysRevE.60.5305
[2]	Pagan, A., The econometrics of financial markets, Journal of Empirical Finance, 48, 1-3, 15-102 (1996)
[3]	Mantegna, R. N.; Stanley, H. E., Scaling behaviour in the dynamics of an economic index, Nature, 376, 6535, 46-49 (1995) · doi:10.1038/376046a0
[4]	Sklar, M., Fonctions de répartition à \(n\) dimensions et leurs marges, 8, 229-231 (1959) · Zbl 0100.14202
[5]	Nelsen, R. B., An Introduction to Copula (1983), New York, NY, USA: Elsevier Science, New York, NY, USA
[6]	Hurst, H. E., Long term storage capacity of reservoirs, Transactions American Society of Civil Engineers, 116, 770-808 (1951)
[7]	Peng, C.-K.; Buldyrev, S. V.; Havlin, S.; Simons, M.; Stanley, H. E.; Goldberger, A. L., Mosaic organization of DNA nucleotides, Physical Review E, 49, 2, 1685-1689 (1994) · doi:10.1103/PhysRevE.49.1685
[8]	Castro E. Silva, A.; Moreira, J. G., Roughness exponents to calculate multi-affine fractal exponents, Physica A: Statistical Mechanics and Its Applications, 235, 3-4, 327-333 (1997) · doi:10.1016/S0378-4371(96)00357-3
[9]	Weber, R. O.; Talkner, P., Spectra and correlations of climate data from days to decades, Journal of Geophysical Research D: Atmospheres, 106, 17, 20131-20144 (2001) · doi:10.1029/2001JD000548
[10]	Kantelhardt, J. W.; Zschiegner, S. A.; Koscielny-Bunde, E.; Havlin, S.; Bunde, A.; Stanley, H. E., Multifractal detrended fluctuation analysis of nonstationary time series, Physica A: Statistical Mechanics and Its Applications, 316, 1-4, 87-114 (2002) · Zbl 1001.62029 · doi:10.1016/S0378-4371(02)01383-3
[11]	Zunino, L.; Figliola, A.; Tabak, B. M.; Pérez, D. G.; Garavaglia, M.; Rosso, O. A., Multifractal structure in Latin-American market indices, Chaos, Solitons and Fractals, 41, 5, 2331-2340 (2009) · doi:10.1016/j.chaos.2008.09.013
[12]	Podobnik, B.; Stanley, H. E., Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series, Physical Review Letters, 100, 8 (2008) · doi:10.1103/PhysRevLett.100.084102
[13]	Zhou, W.-X., Multifractal detrended cross-correlation analysis for two nonstationary signals, Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 77, 6 (2008) · doi:10.1103/PhysRevE.77.066211
[14]	Jiang, Z.-Q.; Zhou, W.-X., Multifractal detrending moving-average cross-correlation analysis, Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 84, 1 (2011) · doi:10.1103/PhysRevE.84.016106
[15]	Gu, G.-F.; Zhou, W.-X., Detrending moving average algorithm for multifractals, Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 82, 1 (2010) · doi:10.1103/PhysRevE.82.011136
[16]	Alessio, E.; Carbone, A.; Castelli, G.; Frappietro, V., Second-order moving average and scaling of stochastic time series, European Physical Journal B, 27, 2, 197-200 (2002)
[17]	Kristoufek, L., Multifractal height cross-correlation analysis: a new method for analyzing long-range cross-correlations, European Physics Letters, 95, 6 (2011) · doi:10.1209/0295-5075/95/68001
[18]	Cheng, W.; Wang, J., Dependence phenomenon analysis of the stock market, European Physics Letters, 102, 1 (2013) · doi:10.1209/0295-5075/102/18004
[19]	Fang, W.; Wang, J., Fluctuation behaviors of financial time series by a stochastic Ising system on a Sierpinski carpet lattice, Physica A: Statistical Mechanics and Its Applications, 392, 18, 4055-4063 (2013) · doi:10.1016/j.physa.2013.04.048
[20]	Fang, W.; Wang, J., Statistical properties and multifractal behaviors of market returns by ising dynamic systems, International Journal of Modern Physics C, 23, 3 (2012) · Zbl 1263.82023 · doi:10.1142/S0129183112500234
[21]	Niu, H.; Wang, J., Volatility clustering and long memory of financial time series and financial price model, Digital Signal Processing, 23, 2, 489-498 (2013) · doi:10.1016/j.dsp.2012.11.004
[22]	Niu, H.; Wang, J., Power-law scaling behavior analysis of financial time series model by voter interacting dynamic system, Journal of Applied Statistics, 40, 10 (2013) · Zbl 1514.62777 · doi:10.1080/02664763.2013.809515
[23]	Wang, J.; Deng, S., Fluctuations of interface statistical physics models applied to a stock market model, Nonlinear Analysis: Real World Applications, 9, 2, 718-723 (2008) · Zbl 1134.91468 · doi:10.1016/j.nonrwa.2006.11.017
[24]	Wang, J.; Wang, Q.; Shao, J., Fluctuations of stock price model by statistical physics systems, Mathematical and Computer Modelling, 51, 5-6, 431-440 (2010) · Zbl 1190.91117 · doi:10.1016/j.mcm.2009.12.003
[25]	Wang, T.; Wang, J.; Zhang, J.; Fang, W., Voter interacting systems applied to Chinese stock markets, Mathematics and Computers in Simulation, 81, 11, 2492-2506 (2011) · Zbl 1218.91176 · doi:10.1016/j.matcom.2011.03.013
[26]	Zhang, J.; Wang, J., Fractal detrended fluctuation analysis of chinese energy markets, International Journal of Bifurcation and Chaos, 20, 11, 3753-3768 (2010) · doi:10.1142/S0218127410028082
[27]	Pei, A.; Wang, J., Nonlinear analysis of return time series model by oriented percolation dynamic system, Abstract and Applied Analysis, 2013 (2013) · Zbl 1420.91552 · doi:10.1155/2013/612738
[28]	Cheng, W. Y.; Wang, J., Nonlinear fluctuation behavior of financial time series model by statistical physics system, Abstract and Applied Analysis, 2014 (2014) · Zbl 1406.91497 · doi:10.1155/2013/612738
[29]	Durrett, R., Lecture Notes on Particle Systems and Percolation, viii+335 (1988), Pacific Grove, Calif, USA: Wadsworth & Brooks, Pacific Grove, Calif, USA · Zbl 0659.60129
[30]	Liggett, T. M., Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, 324, xii+332 (1999), New York, NY, USA: Springer, New York, NY, USA · Zbl 0949.60006 · doi:10.1007/978-3-662-03990-8
[31]	Shao, Y.-H.; Gu, G.-F.; Jiang, Z.-Q.; Zhou, W.-X.; Sornette, D., Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series, Scientific Reports, 2, article 835 (2012) · doi:10.1038/srep00835
[32]	Chen, M.-F., From Markov Chains to Non-Equilibrium Particle Systems, xii+597 (1992), Singapore: World Scientific, Singapore · Zbl 1078.60003 · doi:10.1142/9789812562456
[33]	Grimmett, G., Percolation, 321, xiv+444 (1999), Berlin, Germany: Springer, Berlin, Germany · Zbl 0926.60004 · doi:10.1007/978-3-662-03981-6
[34]	Liggett, T. M., Interacting Particle Systems, 276, xv+488 (1985), New York, NY, USA: Springer, New York, NY, USA · Zbl 0559.60078 · doi:10.1007/978-1-4613-8542-4
[35]	Lamberton, D.; Lapeyre, B., Introduction to Stochastic Calculus Applied to Finance. Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall/CRC Financial Mathematics Series (1996), London, UK: CRC Press, London, UK · Zbl 0898.60002
[36]	Bouyé, E.; Durrleman, V.; Nikeghbali, A., Copula for Finance: A Reading Guide and Applications (2000), London, UK: Financial Econometrics Research Centre, City University Business School, London, UK
[37]	Cherubini, U.; Luciano, E.; Vecchiato, W., Copula Methods in Finance. Copula Methods in Finance, Wiley Finance Series, xvi+293 (2004), Chichester, UK: John Wiley & Sons, Chichester, UK · Zbl 1163.62081 · doi:10.1002/9781118673331
[38]	Lehmann, E. L., Some concepts of dependence, Annals of Mathematical Statistics, 37, 1137-1153 (1966) · Zbl 0146.40601 · doi:10.1214/aoms/1177699260
[39]	Coles, S.; Currie, J.; Tawn, J., Dependence Measures for Extreme Value Analysis (1999), Department of Mathematics and Statistics, Lancaster University
[40]	Hollander, M.; Wolfe, D. A., Nonparametric Statistical Methods, xviii+503 (1973), New York, NY, USA: John Wiley & Sons, New York, NY, USA · Zbl 0277.62030
[41]	Joe, H., Multivariate Models and Dependence Concepts, 73, xviii+399 (1997), London, UK: Chapman & Hall, London, UK · Zbl 0990.62517 · doi:10.1201/b13150
[42]	Blythe, D. J., A rigorous and efficient asymptotic test for power-law cross-correlation (2013)
[43]	Podobnik, B.; Grosse, I.; Horvatić, D.; Ilic, S.; Ivanov, P. C.; Stanley, H. E., Quantifying cross-correlations using local and global detrending approaches, European Physical Journal B, 71, 2, 243-250 (2009) · doi:10.1140/epjb/e2009-00310-5
[44]	Fama, E., Efficient capital markets: a review of theory and empirical work, Journal of Finance, 25, 384-417 (1970)
[45]	Busse, J. A.; Clifton Green, T., Market efficiency in real time, Journal of Financial Economics, 65, 3, 415-437 (2002) · doi:10.1016/S0304-405X(02)00148-4
[46]	Reboredo, J. C.; Rivera-Castro, M. A.; Miranda, J. G. V.; García-Rubio, R., How fast do stock prices adjust to market efficiency? Evidence from a detrended fluctuation analysis, Physica A, 392, 7, 1631-1637 (2013) · doi:10.1016/j.physa.2012.11.038
[47]	Sun, X.; Chen, H.; Wu, Z.; Yuan, Y., Multifractal analysis of Hang Seng index in Hong Kong stock market, Physica A, 291, 1-4, 553-562 (2001) · Zbl 0972.91047 · doi:10.1016/S0378-4371(00)00606-3