Fraktalne własności wielkości obrotów indeksów WIG20, ATX i CAC40: analiza porównawcza

• Autorzy: Gurgul H. , Suder M.

Warianty tytułu

EN

Fractal properties of trading volume of indexes WIG20, ATX i CAC40: comparative analysis

• Języki publikacji: PL

Abstrakty

PL

W artykule przedstawiono wyniki badań empirycznych dotyczących istnienia struktur nieliniowych, a także chaosu deterministycznego w szeregach wolumenów indeksów ATX, WIG20 oraz CAC40 z okresu I 2001-VIII 2008. Wyniki badań nie są jednoznaczne. Otrzymano bowiem wysokie wartości wykładnika Hursta co może świadczyć o tym, że analizowane szeregi czasowe mają strukturę nieliniową. Tezę o występowaniu chaosu, a zwłaszcza tzw. multifraktalni, może też potwierdzać fakt zbieżności wymiaru korelacyjnego przy wzroście wymiaru zanurzenia. Jednakże chociaż wartości największego wykładnika Lapunowa w przypadku szeregów z usuniętym trendem są dodatnie, to jednak są one za małe, aby można mówić o strukturach chaotycznych. Jest to argument przeciwko uznawaniu szeregów wolumenu za struktury chaotyczne. Brak jednoznacznych konkluzji wskazuje na potrzebę dalszych badań w tym zakresie.

EN

In this paper the results of investigations concerning identification of nonlinear structures and deterministic chaos in trading volume time series of ATX, WIG20 and CAC40 indexes from the period I. 2001-VIII. 2008 are presented. The results are partly inconclusive. The values of Hurst coefficient are relatively large. This may be evidence for existence of nonlinear structure in trading volume time series under consideration. This assumption especially concerning existence of so called multifractals supports convergence of correlation dimension as embedding dimension changes. Although the largest Lyapunov exponents are positive numbers there can not be claimed that trading volume time series exhibit chaotic structures, because computed values are to small. Because of inconclusive results obtained in presented investigation there is a necessity to continue the investigations with other methods in order to draw certain conclusions.

Słowa kluczowe

PL

wielkość obrotów; dynamika nieliniowa; wymiar korelacyjny; test BDS; wykładniki Lapunowa

EN

trading volume; chaotic dynamics; correlation dimension; BDS test; Lyapunov exponents

• Wydawca: Wydawnictwa AGH
• Czasopismo: Ekonomia Menedżerska
• Rocznik: 2010
• Tom: nr 8
• Strony: 125--144
• Opis fizyczny: Bibliogr. 57 poz., tab., wykr.

Twórcy

autor

Gurgul H.

• Akademia Górniczo-Hutnicza w Krakowie, Wydział Zarządzania, Samodzielna Pracownia Zastosowań Matematyki w Ekonomii

autor

Suder M.

• Akademia Górniczo-Hutnicza w Krakowie, Wydział Zarządzania, Samodzielna Pracownia Zastosowań Matematyki w Ekonomii

Bibliografia

• [1] Ajinkya B.B., Jain P.C, The behavior of daily stock market trading volume, „Journal of Accounting and Economics" 1989, Vol. 11, s. 331-359.
• [2] Andersen T.G., Return volatility and trading volume: an Information flow interpretation of stochastic volatility, „Journal of Finance" 1996, Vol. 51, s. 169-204.
• [3] Avouyi-Dovi S., Jondeau E., International transmission and volume effects in G5 stock market returns and volatility, BIS Conference Papers, 2000, No. 8, s. 159-174.
• [4] Baillie R.T., Long memory processes and fractional integration in econometrics, „Journal of Econometrics" 1996, Vol. 73, s. 5-59.
• [5] Beran J.A., Statistical methods for data with long-range dependence, „Statistical Science", 1992, Vol. 7, s. 404-427.
• [6] Bernardo A., Judd K.L., Volume and price formation in an asset trading model with asymmetric Information, Working Paper, 1996. Online unter: http://ideas.repec.org/p/cdl/anderf/1136.html.
• [7] Bessembinder H., Seguin P.J., Price volatility, trading volume, and market depth: evidence from futures markets, „Journal of Financial and Quantitative Analysis" 1993, Vol. 28, s. 21-39.
• [8] Blume L., Easley D., O'Hara M., Market statistics and technical analysis: The role of volume, „Journal of Finance" 1994, Vol. 49, s. 153-181.
• [9] Brailsford T.J., The empirical relationship between trading volume, returns and volatility, „Accounting and Finance" 1996, Vol. 35, 89-111.
• [10] Brooks C, Hinich M.J., Smith M. J., Nonlinear evolution in UK stock returns and volume, w: Rothman R. (red.): Nonlinear time series analysis of economic and financial data, Kluwer Academic Publishers, 1999, s. 165-190.
• [11] Brock W.A., LeBaron B.D., A dynamie structural model for stock return volatility and trading volume, „The Review of Economics and Statistics" 1996, Vol. 78, s. 94-110.
• [12] Brock W.A., Hsieh D., LeBaron B.D., A Test of Nonlinear Dynamics, Chaos, and Instability, Cambridge: MIT Press, 1991.
• [13] Campbell J.Y, Grossmann S.J., Wang J., Trading volume and serial correlation in stock returns, „Quarterly Journal of Economics" 1993, Vol. 108, s. 905-939.
• [14] Chordia T, Swaminathan B., Trading volume and cross-autocorrelations in stock returns, „Journal of Finance" Vol. 55, s. 913-935.
• [15] Clark P.K., A subordinated stochastic process model with finite variance for speculative prices, „Econometrica" 1973, Vol. 41, s. 135-156.
• [16] Connolly R., Stivers C, Momentum and reversals in equity-index returns during periods of abnormal turnover and return dispersion, „Journal of Finance" 2003, Vol. 58, s. 1521-1555.
• [17] Copeland T.E., A model of asset trading under the assumption of seąuential information arrival, „Journal of Finance" 1976, Vol. 31, s. 1149-1168.
• [18] Darrat A.F., Rahman S., Zhong M., Intraday trading volume and return volatility of the DJIA stocks: a note, „Journal of Banking and Finance" 2003, Vol. 27, s. 2035-2043.
• [19] Dockner EJ., Prskawetz A., Feichtinger G., Nonlinear Dynamics and Predictability in the Austrian Stock Market, C. Heij et. al. (red.), System Dynamics in Economic and Financial Models, John Wiley Press, 1997, s. 45-62.
• [20] ElsnerJ., Chaos und Zufall am deutschen Aktienmarkt, Heidelberg, Physica-Verlag 1996.
• [21] Epps T.W, Epps M.L., The stochastic dependence of security price changes and transaction volumes: implications for the mixture-of-distribution hypothesis, „Econometrica" 1976, Vol. 44, 305-321.
• [22] Fama E.F.,Efficient capital markets: A review of theory and empirical work, „Journal of Finance" 1970, Vol. 25, s. 383-417.
• [23] Frank M., Gencay R., Stengos T., International chaos?, „European Economic Review" 1988, Vol. 32, s. 1569-1584.
• [24] Gallant A.R., Rossi P.E., Tauchen G., Stock prices and volume, „Review of Financial Studies" 1992, Vol. 5, s. 199-242.
• [25] Gallo G.M., Pacini B., The effects of trading activity on market volatility, „European Journal of Finance" 2000, Vol. 6, s. 163-175.
• [26] Gervais S., Kaniel R., Mingelgrin D.H., The high-volume return premium, „Journal of Finance" 2001, Vol. 56, s. 877-919.
• [27] Geweke J., Porter-Hudak S., The estimation and application of long memory time series models, „Journal of Time Series Analysis" 1983, Vol. 4, s. 221-238.
• [28] Glosten L., Milgrom P, Bid, ask, and transaction prices in a specialist market with heterogeneously informed traders, „Journal of Financial Economics" 1985, Vol. 13, s. 71-100.
• [29] Granger C.W.J., Joyeux R., An introduction to long-memory time series models and fractional differencing „Journal of Time Series Analysis" 1980, Vol. 1, s. 15-29.
• [30] Gurgul H., Suder M., Nieliniowa dynamika indeksów giełdowych WIG20 i ATK: analiza porównawcza, „Ekonomia Menadżerska" 2010, nr 7, s. 103-120.
• [31] Harris L., Transaction data tests of the mixture of distributions hypothesis, „Journal of Financial and Quantitative Analysis" 1987, Vol. 22, s. 127-141.
• [32] Hiemstra C, Jones J.D., Testing for linear and nonlinear Granger causality in the stock price - volume relation, „Journal of Finance" 1994, Vol. 49, s. 1639-1664.
• [33] Hosking J.R.M., Fractional differencing, „Biometrika" 1981, Vol. 68, s. 165-176.
• [34] Hsieh D.A., Chaos and nonlinear dynamics: Applications to financial markets, „Journal of Finance" 1991, Vol. 46, s. 1839-1877.
• [35] Hurst H.E., The Long Term Storage Capacity of Reservoirs, „Transactions of the American Society of Civil Engineers" 1951, 116, s. 770-808.
• [36] Jaditz T., Sayers C.L., Is chaos generic in economic data?. „International Journal of Bifurcations and Chaos" 1993, Vol. 3, s. 745-55.
• [37] Jayaraman N., Frye M.B., Sabherwal S., Informed trading around merger announcements: an empirical test using transaction volume and open interest in options market, „Financial Review" 2001, Vol. 37, s. 45-74.
• [38] Jennings R., Starks L., Fellingham J., An eąuilibrium of asset trading with sequential information arrival, „Journal of Finance" 1981, Vol. 36, s. 143-161.
• [39] Jung R.C., Liesenfeld R., Testing the bivariate mixture hypothesis using German stock market data, „European Financial Management" 1996, Vol. 2, s. 273-297.
• [40] Karpoff J.M., The relation between price changes and trading volume: a survey, „Journal of Financial and Quantitative Analysis" 1987, Vol. 22, s. 109-126.
• [41] Kempf A., Korn O., Preisprognosen mit Handelsvolumen, „Financial Markets and Portfolio Management" 1999, Vol. 13, s. 178-193.
• [42] Kesy C, Informationsverarbeitung am Rentenmarkt, Uhlenbruch-Verlag, 2004.
• [43] Lamoureux C.G., Lastrapes W.D., Heteroskedasticity in stock return data: volume versus GARCH effects, „Journal of Finance" 1990, Vol. 45, s. 221-229.
• [44] Lamoureux C.G., Lastrapes WD., Endogenous trading volume and momentum in stock-return volatility, „Journal of Business and Economic Statistics" 1994, Vol. 12, s. 253-260.
• [45] Lee B.-S., Rui O.M., Does trading volume contain information to predict stock returns?Evidence from China's stock markets, „Review of Quantitative Finance and Accounting" 2000, Vol. 14, s. 341-360.
• [46] Luu J.C., Martens M., Testing the mixture-of-distributions hypothesis using„realized" volatility, „Journal of Futures Markets" 2003, Vol. 23, s. 661-679.
• [47] Mandelbrot B.B., When can a price be arbitraged efficiently? A limit to the validity of the random walk and martingale models, „Review of Economics and Statistics" 1971, Vol. 53, s. 225-236.
• [48] Mandelbrot B.B., van Ness J.W, Fractional Brownian Motion, Fractional Noises and Applications, „SIAM Review" 1968, Vol. 10 (4), s. 422-437.
• [49] McKenzie M.D., Faff R.W, The determinants of conditiona lautocorrelation in stock returns, „Journal of Financial Research" 2003, Vol. 26, s. 259-274.
• [50] Omran M.F., McKenzie E., Heteroscedasticity in stock returns data revisited: volume versus GARCH effects, „Applied Financial Economics" 2000, Vol. 10, s. 553-560.
• [51] Peters E.E., Teoria chaosu a rynki kapitałowe, WIG Press, Warszawa 1997.
• [52] Ray B.K., Tsay R.S., Long-range dependence in daily stock volatilities, „Journal of Business and Economic Statistics" 2000, Vol. 18, s. 254-262.
• [53] Robinson P.M., Semiparametric analysis of long-memory time series, „Annals of Statistics" 1994, Vol. 22, s. 515-539.
• [54] Safvenblad P, Trading volume and autocorrelation: empirical evidence from the Stockholm stock exchange, „Journal of Banking and Finance" 2000, Vol. 24, s. 1275-1287.
• [55] Sowell F.B., Maximum likelihood estimation of stationary univariate fractionally integrated time series models, „Journal of Econometrics" 1992, Vol. 53, s. 165-188.
• [56] Suominen M., Trading volume and information revelation in stock markets, „Journal of Financial and Quantitative Analysis" 2001, Vol. 36, s. 545-565.
• [57] Tauchen G.E., Pitts M., The price variability - volume relationship on speculative markets, „Econometrica" 1983, Vol. 51, s. 485-505.