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Abstract
In this paper, we propose a method using continuous wavelets to study the multivariate fractional Brownian motion through the deviations of the transformed random process to find an efficient estimate of Hurst exponent using eigenvalue regression of the covariance matrix. The results of simulations experiments shown that the performance of the proposed estimator was efficient in bias but the variance get increase as signal change from short to long memory the MASE increase relatively. The estimation process was made by calculating the eigenvalues for the variance-covariance matrix of Meyer’s continuous wavelet details coefficients.
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References
- Abry, P. and Sellan, F., (1996), “The wavelet-based synthesis for fractional Brownian motion proposed by F. Sellan and Y. Meyer: remarks and fast implemention”, Applied and computational harmonic analysis, Vol. 3, pp. 377-383.
- Abry, P. and Didier, G., (2018), “Wavelet estimation for operator fractional Brownian motion”, Bernoulli, Vol. 24, No. 2, pp. 895-928.
- Ayache A. and Vehel J. L., (2000), “The Generalized Multifractional Brownian Motion”, Statistical Inference for Stochastic Processes, Vol. 3, pp. 7-18.
- Cambanis, S. and Houdre, C., (1995), “On the Continuous wavelet transform of second order random processes”, IEEE Transactions on information theory, Vol. 41, No. 3, pp. 628-643.
- Debnath, L. and Ahmad Shah, F., (2015), “Wavelet transforms and their applications”, Springer New York Heidelberg Dordrecht London, 2nd edition.
- Daubechies, I., (1999), “Ten lectures on Wavelets”, Society for Industrial and Applied Mathematics, 6th edition.
- Hmood, M. Y. and Jumma, M., (2020), “Use of Le'vy's Model to Simulate Stock Dividends Actual Estimations of Some Iraqi Banks”, May 2020 International Journal of Psychosocial Rehabilitation Vol. 24, No. 9, pp. 83-97.
- Hmood, M. Y., (2016), “Using the Le'vy Model to estimate the stock returns for some Iraqi banks” April 2016, Journal of Economics and Administrative Sciences, Vol. 22, No. 94, pp. 460- 479.
- Hmood, M. Y. and Amir, Y., (2020), “Estimation of return stock rate by using wavelet and kernel smoothers” Periodicals of Engineering and Natural Sciences (PEN), Vol. 8, No. 2, pp. 602-612.
- Mallat, S., (2009), “A Wavelet tour of signal processing: the sparse way”, Elsevier Inc., 3rd edition.
- Mandelbrot, B. B. & Van Ness, J., (1968), “Fractional Brownian motion, fractional noises and applications”, IBM Watson Research Center, Vol. 10, No. 4, pp. 422-437.
- Nourdin, I., (2012), “selected aspects of fractional Brownian motion”, B&SS – Bocconi & Springer Series.
- Perrin, E., Harba, R., Berzin-Joeseph, C., Iribarren, I. and Bonami, A., (2001), “nth-order fractional Brownian motion and fractional Gaussian noises”, IEEE Transactions on signal processing, Vol. 49, No. 5, pp. 1049-1059.
- Power, G. J. and Turvey, G. C., (2010), “Long-range dependence in the volatility of commodity futures prices: wavelet-base evidence”, Phys. A., Vol. 389, pp. 79-90.
- Vermehren, V. and de Oliveira, Hélio, (2015), “Close expressions for Meyer Wavelet and Scale Function” Anais de XXXIII Simpósio Brasileiro de Telecomunicações pp. 4-8.
- Wu, L. and Ding, Y., (2017), “Wavelet-based estimator for the hurst parameters of fractional Brownian sheet”, Vol. 37, pp. 205-222.