American Journal of Applied Mathematics

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Wavelets in the Analysis of Autoregressive Conditional Heteroskedasticity (ARCH) Models Using Neural Network

Received: 29 February 2016    Accepted: 15 March 2016    Published: 30 March 2016
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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.

DOI 10.11648/j.ajam.20160402.14
Published in American Journal of Applied Mathematics (Volume 4, Issue 2, April 2016)
Page(s) 92-98
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Signal Analysis, Discrete Wavelet Transform, Frequency Decomposition, Regression Analysis, ARCH Model, Neural Network

References
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Author Information
  • Department of Mathematics, HKBK College of Engineering, Bangalore, India

  • Department of Mechanical Engineering, Umm Al-Qura University, College of Engineering and Islamic Architecture, Makkah, Kingdom of Saudi Arabia

  • Department of Mechanical Engineering, Umm Al-Qura University, College of Engineering and Islamic Architecture, Makkah, Kingdom of Saudi Arabia

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  • APA Style

    Ataulla, Mohammed Yunus, Mohammad S. Alsoufi. (2016). Wavelets in the Analysis of Autoregressive Conditional Heteroskedasticity (ARCH) Models Using Neural Network. American Journal of Applied Mathematics, 4(2), 92-98. https://doi.org/10.11648/j.ajam.20160402.14

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    ACS Style

    Ataulla; Mohammed Yunus; Mohammad S. Alsoufi. Wavelets in the Analysis of Autoregressive Conditional Heteroskedasticity (ARCH) Models Using Neural Network. Am. J. Appl. Math. 2016, 4(2), 92-98. doi: 10.11648/j.ajam.20160402.14

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    AMA Style

    Ataulla, Mohammed Yunus, Mohammad S. Alsoufi. Wavelets in the Analysis of Autoregressive Conditional Heteroskedasticity (ARCH) Models Using Neural Network. Am J Appl Math. 2016;4(2):92-98. doi: 10.11648/j.ajam.20160402.14

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  • @article{10.11648/j.ajam.20160402.14,
      author = {Ataulla and Mohammed Yunus and Mohammad S. Alsoufi},
      title = {Wavelets in the Analysis of Autoregressive Conditional Heteroskedasticity (ARCH) Models Using Neural Network},
      journal = {American Journal of Applied Mathematics},
      volume = {4},
      number = {2},
      pages = {92-98},
      doi = {10.11648/j.ajam.20160402.14},
      url = {https://doi.org/10.11648/j.ajam.20160402.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.20160402.14},
      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.},
     year = {2016}
    }
    

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    AU  - Ataulla
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    AB  - 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.
    VL  - 4
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