| Reference: | Arneodo, A., Grasseau, G., and Holschneider, M., “Wavelet Transform of Multifractals,” Physical Review Letters, v61, # 20, November (1988), 2281-2284.
Arneodo, A., Barry, E., J. Delour., Muzy, J. F., The thermodynamics of fractals revisited with wavelets, Physica A, 213, 232-275 (1995).
Arneodo, A., Bacry, E., Muzy, J. F.,“Random cascades on wavelet dyadic trees,”Journal of Mathematical Physics, v39, # 8, August (1998), 4142-4164.
Audit, B., Barry, E., Muzy, J. F., Arneodo, A., (2002), Wavelet based estimator of scaling behavior, IEEE. in Information Theory 48, 11, pp 2938-2954.
Barry, E., J. Delour., Muzy, J. F., Modelling financial time series using multifractal random walks., Physica A, 299, 84-92 (2001).
Baillie, R. T., “Long Memory Processes and Fractional Integration in Econometrics,” Journal of Econometrics 73:1 (1996), 5–59.
Baillie, R. T., T. Bollerslev, and H. O. Mikkelsen, “Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics 74:1 (1996), 3–30.
Baillie, R. T., C. F. Chung, and M. A. Tieslau, “Analyzing Inflation by the Fractionally Integrated ARFIMA-GARCH Model,” Journal of Applied Econometrics 11:1 (1996), 23–40.
Billingsley, P., Probability and Measure, (New York: John Wiley and Sons, 1995).
Billingsley, P., Convergence of Probability Measures, (New York: John Wiley and Sons, 1999).
Bollerslev, T., “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics 31:3 (1986), 307–327.
Breidt, F.J., Crato, N. and P. de Lima, 1998, The detection and estimation of long
memory in stochastic volatility, Journal of Econometrics, 83, pp.325-348.
Calvet, L., A. Fisher, and B. B. Mandelbrot, “Large Deviation Theory and the Distribution of Price Changes,” Cowles Foundation discussion paper no. 1165, Yale University, available from the SSRN database at http://www.ssrn.com (1997).
Calvet, L., and A. Fisher, “Forecasting Multifractal Volatility,” Journal of Econometrics 105:1 (2001), 27–58.
Calvet, L., and A. Fisher, “Multifractality in Asset Returns: Theory and Evidence,” Review of Economics and Statistics 84 (2002), 381--406.
Calvet, L., and A. Fisher,“How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes,” Journal of Financial Econometrics, 2 (2004), 49--83
Campbell, J., A. Lo, and A. C. MacKinlay, The Econometrics of Financial Markets (Princeton: Princeton University Press, 1997).
Engle, R. F., “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom In ation,” Econometrica 50:4 (1982), 987–1007.
Engle, R.F. and T. Bollerslev, 1986, Modeling the persistence of conditional
variance, Econometric Reviews, 5, pp.1-50.
Falconer, K. Fractal Geometry: Mathematical Foundations and Applications, (New
York: John Wiley and Sons, 1990)
Fisher, A., L. Calvet, and B. B. Mandelbrot, “Multifractality of Deutsche Mark/US Dollar Exchange Rates,” Cowles Foundation discussion paper no. 1166, Yale University, available from the SSRN database at http://www.ssrn.com (1997).
Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh, Mark RG, Mietus JE, Moody GB, Peng C-K, Stanley HE. PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals. Circulation101(23):e215-e220[CirculationElectronicPages;http://circ.ahajournals.org/cgi/content/full/101/23/e215]; 2000 (June 13).
Lo, A. W., “Long Memory in Stock Market Prices,” Econometrica 59:5 (1991), 1279–1313.
Mandelbrot, B. B., A. Fisher, and L. Calvet, “The Multifractal Model of Asset Returns,” Cowles Foundation discussion paper no. 1164, Yale University, paper available from the SSRN database at http://www.ssrn.com (1997).
Mandelbrot, B. B., and J. W. van Ness, “Fractional Brownian Motion, Fractional Noises and Application, ” SIAM Review 10:4 (1968), 422–437.
Mandelbrot, B.B, Fractals and Scaling in Finance: Discontinuity, Concetration, Risk. Springer, New York (1997).
Muzy, J. F., Bacry, E. and A. Arneodo, Wavelets and Multifractal Formalism for Singular Signals: Application to Turbulence Data, Physical Review Letters, v. 67, # 25, December (1991), pp. 3515-3518.
Muzy, J.F., Bacry ,E. and A. Arneodo,Multifractal formalism for fractal signals. The structure-function approach versus the wavelet-transform modulus-maxima method, Phys. Rev. E 47, 875 (1993).
X. S., Huiping C., Ziqin W., Yongzhuang Yuan, Multifractal analysis of Hang Seng index inHong Kong stockmark et, Phys. A 291 (2001) 553–562.
X. S., Huiping C.,Yongzhuang Y., Ziqin W., Predictability of multifractal analysis of Hang Seng stockindex in Hong Kong, Phys. A 301 (2001) 473–482.
Yu W., Dengshi H., Multifractal analysis of SSEC in Chinese stock market: A different empirical result from Heng Seng index, Phys. A 355 (2005) 497-508. |
