Wavelets in the Analysis of Autoregressive Conditional Heteroskedasticity (ARCH) Models Using Neural Network
American Journal of Applied Mathematics
Volume 4, Issue 2, April 2016, Pages: 92-98
Received: Feb. 29, 2016; Accepted: Mar. 15, 2016; Published: Mar. 30, 2016
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Authors
Ataulla , Department of Mathematics, HKBK College of Engineering, Bangalore, India
Mohammed Yunus, Department of Mechanical Engineering, Umm Al-Qura University, College of Engineering and Islamic Architecture, Makkah, Kingdom of Saudi Arabia
Mohammad S. Alsoufi, Department of Mechanical Engineering, Umm Al-Qura University, College of Engineering and Islamic Architecture, Makkah, Kingdom of Saudi Arabia
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Abstract
In the paper, proposed a new method for the time frequency signal analysis, speech processing and other signal processing applications. Stationary signal components can be analyzed by a powerful tool called as Fourier transform. But it is fizzled for analysing the non-stationary signal whereas wavelet transform allows the components of a non-stationary signal to be analyzed. It is the improved version of Fourier transform. Wavelets allow complex information such as music, speech, images and patterns to be decomposed into elementary forms at different positions and scales and subsequently reconstructed with high precision. Here, for extracting the best features of non-stationary signal we use discrete wavelet transform. This can be decomposed into two components named as high frequency component and low frequency component. The decomposed output component is sent for regression analysis. This is done by passing through ARCH model which can characterize and model observed time series. An ARCH time series is the one in which the variance of the error in a period depends on upon size of the squared error in the previous period i.e. if a large error occurs in one period, the variance of the error in the next period will be even larger. The performance of the ARCH will be improved by predicting its co-efficient or cofactor using an artificial technique. The artificial technique presented in this paper is neural network, which is capable of handling sophisticated computations similar to the human brain. The proposed model algorithm will be implemented in MATLAB and the output performances are estimated.
Keywords
Signal Analysis, Discrete Wavelet Transform, Frequency Decomposition, Regression Analysis, ARCH Model, Neural Network
To cite this article
Ataulla , Mohammed Yunus, Mohammad S. Alsoufi, Wavelets in the Analysis of Autoregressive Conditional Heteroskedasticity (ARCH) Models Using Neural Network, American Journal of Applied Mathematics. Vol. 4, No. 2, 2016, pp. 92-98. doi: 10.11648/j.ajam.20160402.14
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Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
Jian Li, “Spectral Estimation”, Department of Electrical and Computer Engineering University of Florida Gainesville, FL 32611, USA.
[2]
Jonas Buchli, Ludovic Righetti and Auke Jan Ijspeert, “Frequency analysis with coupled nonlinear oscillators”, Physica D: Nonlinear Phenomena, Volume 237, No. 13, 1 August, Pg 1705–1718, 2008.
[3]
R. J. E. Merry, “Wavelet Theory and Applications”, A literature study, Eindhoven, June 7 2005.
[4]
M. Misiti, Y. Misiti, G. Oppenheim, and J-M Poggi, “Wavelets Toolbox Users Guide: The Math Works”, Wavelet Toolbox for use with MATLAB, 2000.
[5]
M. Sifuzzaman, M. R. Islam and M. Z. Ali, “Application of Wavelet Transform and its Advantages Compared to Fourier Transform”, Journal of Physical Sciences, Vol. 13, 121-134, 2009.
[6]
Pascal Yiou, Didier Sornette, Michael Ghil, “Data-adaptive wavelets and multi-scale singular-spectrum analysis”, Physica D 142, 254–290, 2000.
[7]
D. B. Pawar, R. S. Kawitkar, M. Selva Balan, “Wavelet Analysis for Processing of Earthquake Records”, International Journal of Science and Technology, Volume 2 No.5, May 2012.
[8]
G. Ranganathan, R. Rangarajan, V. Bindhu, “ECG Signal Analysis for Mental Stress Assessment using Wavelets and Fuzzy Clustering”, European Journal of Scientific Research, Vol.65, No.2, pp. 268-280, 2011.
[9]
Abdul Karim, Samsul Ariffin, Bakri Abdul Karim, M Tahir Ismail, M Khatim Hasan, Jumat Sulaiman, “Applications of Wavelet Method in Stock Exchange Problem”, Journal of Applied Sciences 01/2011.
[10]
R. F. Engle, “Autoregressive conditional heteroskedasticity with estimates of the variance of united kingdom inflation”, Econometrica 50, pp. 987–1007, July 1982.
[11]
T. Bollerslev, “Generalized autoregressive conditional heteroskedasticity”, J. Econometrics 31 (3), 307–327, April 1986.
[12]
T. Bollerslev, R. Y. Chou Kenneth, F. Kroner, ARCH modeling in finance: A review of the theory and empirical evidence, J. Econometrics 52 (1–2), 5–59, April–May 1992.
[13]
Israel Cohen, “Modelling speech signals in the time–frequency domain using GARCH”, Signal Processing 84, 2453–2459, 2004.
[14]
Israel Cohen, “Speech spectral modeling and enhancement based on autoregressive conditional heteroscedasticity models”, Elsevier, Signal processing, Volume 86, Issue 4, Pages 698-709, 2006/4/30.
[15]
P. Campolucci, A. Uncini, F. Piazza, “Fast Adaptive IIR-MLP Neural Networks for Signal Processing Application”, Proceedings of IEEE Int. Conference on Acoustic Speech and Signal Processing, Atlanta, USA, 7-10 May 1996.
[16]
Aurelio Uncini, “Audio signal processing byneural networks”, Elsevier / Neurocomputing, 593–625, 2003.
[17]
RJ Frank, Neil Davey, SP Hunt, “Time series prediction and neural networks”, Journal of Intelligent & Robotic Systems, Volume 31, Issue 1, Pages 91-103, 2001/5/1.
[18]
GP Zhang1and VL Berardi, “Time series forecasting with neural network ensembles: an application for exchange rate prediction”, Journal of the Operational Research Society, 52, 652-664, 2001.
[19]
AK Dhamija, VK Bhalla, “Financial Time Series Forecasting: Comparison of Neural Networks and ARCH Models”, International Research Journal of Finance and Economics, Issue 49, 2010.
[20]
Mohammed Awad, “Chaotic Time series Prediction using Wavelet Neural Network”, Journal of Artificial Intelligence: Theory and Application, Vol.1, Iss.3, pp. 73-80, 2010.
[21]
Juan Peralta, Xiaodong Li, German Gutierrez, Araceli Sanchis, “Time series forecasting by evolving artificial neural networks using genetic algorithms and differential evolution”, IEEE World Congress on Computational Intelligence, 18-23, July-2010.
[22]
A. Lendasse, E. De Bodt, V. Wertz, And M. Verleysen, “Non-linear financial time series forecasting – Application to the Bel 20 stock market index”, European Journal of Economic and Social Systems 14 N° 1, 81-91, 2000.
[23]
Hanh H. Nguyen Æ Christine W. Chan, “Multiple neural networks for a long term time series forecast”, Neural Comput & Applic No.13, 90–98, 2004.
[24]
Petr Sysel, Jiri Misurec, “Estimation of Power Spectral Density using Wavelet Thresholding”, Proceedings of the 7th WSEAS International Conference on CIRCUITS, SYSTEMS, ELECTRONICS, CONTROL and SIGNAL PROCESSING, 2008.
[25]
Youngchan Kim, Kyung Hwan Jin, Jong Chul Ye, Jaewook Ahn, and Dae-Su Yee, “Wavelet Power Spectrum Estimation for High-resolution Terahertz Time-domain Spectroscopy” Journal of the Optical Society of Korea, Vol. 15, No. 1, pp. 103-108, March 2011.
[26]
Tariq Abu Hilal , Hasan Abu Hilal, Riyad El Shalabi and Khalid Daqrouq, “Speaker Verification System Using Discrete Wavelet Transform And Formants Extraction Based On The Correlation Coefficient”, Proceedings of the International MultiConference of Engineering and Computer Scientists, Vol II, 2011.
[27]
Wasim Ahmad, Hüseyin Hacıhabibo˘gluy, and Ahmet M. Kondoz, “DISCRETE WAVELET TRANSFORM BASED SHIFT-INVARIANT ANALYSIS SCHEME FOR TRANSIENT SOUND SIGNALS”, Proc. of the 13th Int. Conference on Digital Audio Effects, September 6-10, 2010.
[28]
Lakshmanan M. K, Ariananda D. D, Nikookar, H, “A reconfigurable wavelet packet filter bank transceiver for spectral analysis and dynamic spectrum access”, IEEE Symposium on Communication, Networking & Broadcasting ; Computing & Processing, 564-575, 3-6 May 2011.
[29]
Fulufhelo V. Nelwamondo, Tshilidzi Marwala, “Handling Missing Data from Heteroskedastic and Nonstationary Data” Advances in Neural Networks – ISNN 2007, Lecture Notes in Computer Science Vol. 4491, pp 1293-1302, 2007.
[30]
Carmen Vidal, Alberto Suárez, “Hierarchical Mixtures of Autoregressive Models for Time-Series Modeling” Artificial Neural Networks and Neural Information Processing, Lecture Notes in Computer Science Vol. 2714, pp 597-604, 2003.
[31]
Junghwan Jin and Jinsoo Kim Forecasting Natural Gas Prices Using Wavelets, Time Series, and Artificial Neural Networks, Journal plosone, November 5, 2015. doi: http:\\ DOI: 10.1371/journal.pone.0142064.
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