Using Excel to Simulate and Visualize Conditional Heteroskedastic Models

William Henry Laverty; Ivan William Kelly

doi:doi:10.11648/j.ajtas.20180706.17

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Using Excel to Simulate and Visualize Conditional Heteroskedastic Models

William Henry Laverty, Ivan William Kelly

Published in American Journal of Theoretical and Applied Statistics (Volume 7, Issue 6)

Received: 29 October 2018 Accepted: 21 November 2018 Published: 18 December 2018

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Abstract

Longitudinal data are available in many disciplines, and quite often the mechanism generating the data are changing over time. These changes must be accounted for when modelling the data and subsequently drawing conclusions from the data. The three statistical models described in this article (GARCH, HMM, ARHMM) are appropriate modelling data with such changes. These three models are generalizations of a random walk. In a random walk the random changes over time have a constant distribution. The three models illustrated account for changes in the distribution of the random displacements over time. Our purpose in the article is to illustrate these three models and their intricacies using Excel. We would also contend and encourage the application of these three models to the analysis of other continuous data in fields utilizing social and medical data.

Published in	American Journal of Theoretical and Applied Statistics (Volume 7, Issue 6)
DOI	10.11648/j.ajtas.20180706.17
Page(s)	242-246
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), 2018. Published by Science Publishing Group

Keywords

Time Series Analysis, GARCH, Hidden Markov Models (HMM), Autoregressive Hidden Markov (ARHMM), Simulation, Excel

References

[1]	B. G. Malkiel (1973) A Random Walk Down Wall Street. W. W. Norton. New York (NY).
[2]	R. S. Tsay (2010) Analysis of Financial Time Series. Third Edition. Wiley. Hoboken (NJ).
[3]	W. H. Laverty, M. J. Miket, and I. W. Kelly. (2002). Simulation of Hidden Markov Models with EXCEL, Journal of Royal Statistical Society. Series D. 51: 31-40.
[4]	I. Visser, M. E. J Raijmakers and P. C. M Molenaar (2002) Fitting Hidden Markov Models to psychological data. Scientific Programming. 10: 185-199. DOI: 10.1109/ICMEW.2013.6618397.
[5]	G. S. Fishman (1995) Monte Carlo, Concepts, Algorithms and Applications. Springer, NewYork (NY).
[6]	M. Walker II, (2011) Hidden Markov Models for Heart Rate Variability with Biometric Applications. All Theses and Dissertations (ETDs). 491.
[7]	R. Mamon, Elliott. (2007) Hidden Markov Models in Finance. International Series n Operations Research and Management Science. Springer. New York. (NY).
[8]	W. H. Laverty, M. J. Miket, and I. W. Kelly IW. (2002) Application of Hidden Markov Models on residuals: an example using Canadian traffic accident data. Perceptual and Motor Skills. 94(3 Pt 2): 1151-6.
[9]	W. H. Laverty, M. J. Miket, and I. W. Kelly. (2002) Examination of Residuals to Vancouver Crisis Call Data by using Hidden Markov Models. Perceptual and Motor Skills. 94: 548-550.
[10]	M. Washha, A. Qaroush, M. Mezghani, and F. Sedes (2017) A Topic-Based Hidden Markov Model for Real-Time Spam Tweets Filtering. 21st International Conference on Knowledge Based and Intelligent Information and Engineering Systems, 6-8 September, Marseille, France.
[11]	B. H. Juang & L. R. Rabiner (1986) Mixture autoregressive hidden Markov models for speech signal, IEEE Transactions on Acoustics Speech and Signal Processing. 33(6): 1404 – 1413.
[12]	X. Tang. (2004). Autoregressive Hidden Markov Model with Application in an El Nin ̃o study. Master’s thesis, University of Saskatchewan, Saskatoon, Saskatchewan, Canada.
[13]	I. Stanculescu, C. K. I Williams, and Y. Freer. (2013). Autoregressive Hidden Markov Models for the Early Detection of Neonatal Sepsis. Biomedical and Health Informatics, IEEE Journal of Biomedical and Health Informatics. 18: 1560-1570. DOI 10.1109/JBHI.2013.2294692.

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APA Style

William Henry Laverty, Ivan William Kelly. (2018). Using Excel to Simulate and Visualize Conditional Heteroskedastic Models. American Journal of Theoretical and Applied Statistics, 7(6), 242-246. https://doi.org/10.11648/j.ajtas.20180706.17

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ACS Style

William Henry Laverty; Ivan William Kelly. Using Excel to Simulate and Visualize Conditional Heteroskedastic Models. Am. J. Theor. Appl. Stat. 2018, 7(6), 242-246. doi: 10.11648/j.ajtas.20180706.17

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AMA Style

William Henry Laverty, Ivan William Kelly. Using Excel to Simulate and Visualize Conditional Heteroskedastic Models. Am J Theor Appl Stat. 2018;7(6):242-246. doi: 10.11648/j.ajtas.20180706.17

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@article{10.11648/j.ajtas.20180706.17,
  author = {William Henry Laverty and Ivan William Kelly},
  title = {Using Excel to Simulate and Visualize Conditional Heteroskedastic Models},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {6},
  pages = {242-246},
  doi = {10.11648/j.ajtas.20180706.17},
  url = {https://doi.org/10.11648/j.ajtas.20180706.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180706.17},
  abstract = {Longitudinal data are available in many disciplines, and quite often the mechanism generating the data are changing over time. These changes must be accounted for when modelling the data and subsequently drawing conclusions from the data. The three statistical models described in this article (GARCH, HMM, ARHMM) are appropriate modelling data with such changes. These three models are generalizations of a random walk. In a random walk the random changes over time have a constant distribution. The three models illustrated account for changes in the distribution of the random displacements over time. Our purpose in the article is to illustrate these three models and their intricacies using Excel. We would also contend and encourage the application of these three models to the analysis of other continuous data in fields utilizing social and medical data.},
 year = {2018}
}

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TY  - JOUR
T1  - Using Excel to Simulate and Visualize Conditional Heteroskedastic Models
AU  - William Henry Laverty
AU  - Ivan William Kelly
Y1  - 2018/12/18
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180706.17
DO  - 10.11648/j.ajtas.20180706.17
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 242
EP  - 246
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SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180706.17
AB  - Longitudinal data are available in many disciplines, and quite often the mechanism generating the data are changing over time. These changes must be accounted for when modelling the data and subsequently drawing conclusions from the data. The three statistical models described in this article (GARCH, HMM, ARHMM) are appropriate modelling data with such changes. These three models are generalizations of a random walk. In a random walk the random changes over time have a constant distribution. The three models illustrated account for changes in the distribution of the random displacements over time. Our purpose in the article is to illustrate these three models and their intricacies using Excel. We would also contend and encourage the application of these three models to the analysis of other continuous data in fields utilizing social and medical data.
VL  - 7
IS  - 6
ER  -

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Author Information

William Henry Laverty

Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Canada
Ivan William Kelly

Department of Educational Psychology & Special Education, University of Saskatchewan, Saskatoon, Canada

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APA Style

William Henry Laverty, Ivan William Kelly. (2018). Using Excel to Simulate and Visualize Conditional Heteroskedastic Models. American Journal of Theoretical and Applied Statistics, 7(6), 242-246. https://doi.org/10.11648/j.ajtas.20180706.17

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ACS Style

William Henry Laverty; Ivan William Kelly. Using Excel to Simulate and Visualize Conditional Heteroskedastic Models. Am. J. Theor. Appl. Stat. 2018, 7(6), 242-246. doi: 10.11648/j.ajtas.20180706.17

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AMA Style

William Henry Laverty, Ivan William Kelly. Using Excel to Simulate and Visualize Conditional Heteroskedastic Models. Am J Theor Appl Stat. 2018;7(6):242-246. doi: 10.11648/j.ajtas.20180706.17

Copy | Download

@article{10.11648/j.ajtas.20180706.17,
  author = {William Henry Laverty and Ivan William Kelly},
  title = {Using Excel to Simulate and Visualize Conditional Heteroskedastic Models},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {6},
  pages = {242-246},
  doi = {10.11648/j.ajtas.20180706.17},
  url = {https://doi.org/10.11648/j.ajtas.20180706.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180706.17},
  abstract = {Longitudinal data are available in many disciplines, and quite often the mechanism generating the data are changing over time. These changes must be accounted for when modelling the data and subsequently drawing conclusions from the data. The three statistical models described in this article (GARCH, HMM, ARHMM) are appropriate modelling data with such changes. These three models are generalizations of a random walk. In a random walk the random changes over time have a constant distribution. The three models illustrated account for changes in the distribution of the random displacements over time. Our purpose in the article is to illustrate these three models and their intricacies using Excel. We would also contend and encourage the application of these three models to the analysis of other continuous data in fields utilizing social and medical data.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Using Excel to Simulate and Visualize Conditional Heteroskedastic Models
AU  - William Henry Laverty
AU  - Ivan William Kelly
Y1  - 2018/12/18
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180706.17
DO  - 10.11648/j.ajtas.20180706.17
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 242
EP  - 246
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180706.17
AB  - Longitudinal data are available in many disciplines, and quite often the mechanism generating the data are changing over time. These changes must be accounted for when modelling the data and subsequently drawing conclusions from the data. The three statistical models described in this article (GARCH, HMM, ARHMM) are appropriate modelling data with such changes. These three models are generalizations of a random walk. In a random walk the random changes over time have a constant distribution. The three models illustrated account for changes in the distribution of the random displacements over time. Our purpose in the article is to illustrate these three models and their intricacies using Excel. We would also contend and encourage the application of these three models to the analysis of other continuous data in fields utilizing social and medical data.
VL  - 7
IS  - 6
ER  -

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