Measuring the Forecast Performance of GARCH and Bilinear-GARCH Models in Time Series Data

Akintunde Mutairu Oyewale; D. K. Shangodoyin; P. M Kgosi

doi:doi:10.11648/j.ajam.20130101.14

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Measuring the Forecast Performance of GARCH and Bilinear-GARCH Models in Time Series Data

Akintunde Mutairu Oyewale, D. K. Shangodoyin, P. M Kgosi

Published in American Journal of Applied Mathematics (Volume 1, Issue 1)

Received: 6 May 2013 Accepted: Published: 30 May 2013

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Abstract

In most of the literature in time series modeling, generalized autoregressive conditional heterosceasticity (GARCH) models has been used as a traditional model to forecast both the economic and financial time series data. Though literature has shown that it is not suitable for non-linear time series. For this reason, this model was augmented with bilinear model in order to make it more relevant in forecasting both economic and financial time series data. After the augmentation, the new model called Bilinear-GARCH (BL-GARCH) shows a better performance based on performance measures indices, models variances and out-of–samples forecast performances. In term of these three criteria the new models outperformed the traditional or classical GARCH model. To drive home this point, these two models were illustrated with Botswana inflation rates data. We observed that the new model (BL-GARCH) outperformed the classical GARCH model.

Published in	American Journal of Applied Mathematics (Volume 1, Issue 1)
DOI	10.11648/j.ajam.20130101.14
Page(s)	17-23
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

GARCH Models, BL-GARCH Models, Forecasting, Inflation Rates and Non-Linear

References

[1]	Anderson T.G.,Bollerslev,T. and Diebold, F.X. (2003) parametric and non parametric volatility measurement. In handbook of financial Econometrics (eds Y. AIT-SAHALIA and L.P Hansen). Amsterdam: North-Holland press.
[2]	Anderson T. W. (2003) Estimation for Autoregressive Moving Average Models in the Time and Frequency Domains. The Ann. of Stat. Vol 5 No. 5, 842-865
[3]	Anderson, T. W. (1977) The Statistical Analysis of Time Series, New York and London Wiley.
[4]	Bonilla, C., Romero-Meza, R. and Hinich, M. J. (2006) Episodic nonlinearities in the Latin American stock market indices, Applied Economics Letters, 13, 195–9.
[5]	Box, G. E. P. and G.M. Jenkins (1970) Time Series, Forecasting and Control. Holden-Day: San Francisco.
[6]	Bruni, C., Dupillo, G. and Koch, G. (1974) Bilinear Systems: An Appealing Class of Nearly Linear System in Theory and Application. IEEE Trans. Auto Control Ac-19, 334-338.
[7]	Engle, R.F. (1982). Autoregressive Conditional Heteroscedasticity with estimates of variance of United Kingdom inflation. Econometrica, 50(4), 987-1007. Baillie, R.
[8]	Nelson, D.B. (1991). Conditional heteroscedasticity in asset returns: A new approach.
[9]	Econometrica, 59(2), 347-370.
[10]	Poon, S.H., Granger, C.W.J. (2003). Forecasting financial market volatility: A review.
[11]	Journal of Economic Literature, 41(2), 478-539(62).

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APA Style

Akintunde Mutairu Oyewale, D. K. Shangodoyin, P. M Kgosi. (2013). Measuring the Forecast Performance of GARCH and Bilinear-GARCH Models in Time Series Data. American Journal of Applied Mathematics, 1(1), 17-23. https://doi.org/10.11648/j.ajam.20130101.14

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ACS Style

Akintunde Mutairu Oyewale; D. K. Shangodoyin; P. M Kgosi. Measuring the Forecast Performance of GARCH and Bilinear-GARCH Models in Time Series Data. Am. J. Appl. Math. 2013, 1(1), 17-23. doi: 10.11648/j.ajam.20130101.14

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AMA Style

Akintunde Mutairu Oyewale, D. K. Shangodoyin, P. M Kgosi. Measuring the Forecast Performance of GARCH and Bilinear-GARCH Models in Time Series Data. Am J Appl Math. 2013;1(1):17-23. doi: 10.11648/j.ajam.20130101.14

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@article{10.11648/j.ajam.20130101.14,
  author = {Akintunde Mutairu Oyewale and D. K. Shangodoyin and P. M Kgosi},
  title = {Measuring the Forecast Performance of GARCH and Bilinear-GARCH Models in Time Series Data},
  journal = {American Journal of Applied Mathematics},
  volume = {1},
  number = {1},
  pages = {17-23},
  doi = {10.11648/j.ajam.20130101.14},
  url = {https://doi.org/10.11648/j.ajam.20130101.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20130101.14},
  abstract = {In most of the literature in time series modeling, generalized autoregressive conditional heterosceasticity (GARCH) models has been used as a traditional model to forecast both the economic and financial time series data. Though literature has shown that it is not suitable for non-linear time series. For this reason, this model was augmented with bilinear model in order to make it more relevant in forecasting both economic and financial time series data. After the augmentation, the new model called Bilinear-GARCH (BL-GARCH) shows a better performance based on performance measures indices, models variances and out-of–samples forecast performances. In term of these three criteria the new models outperformed the traditional or classical GARCH model. To drive home this point, these two models were illustrated with Botswana inflation rates data. We observed that the new model (BL-GARCH) outperformed the classical GARCH model.},
 year = {2013}
}

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TY - JOUR
T1 - Measuring the Forecast Performance of GARCH and Bilinear-GARCH Models in Time Series Data
AU - Akintunde Mutairu Oyewale
AU - D. K. Shangodoyin
AU - P. M Kgosi
Y1 - 2013/05/30
PY - 2013
N1 - https://doi.org/10.11648/j.ajam.20130101.14
DO - 10.11648/j.ajam.20130101.14
T2 - American Journal of Applied Mathematics
JF - American Journal of Applied Mathematics
JO - American Journal of Applied Mathematics
SP - 17
EP - 23
PB - Science Publishing Group
SN - 2330-006X
UR - https://doi.org/10.11648/j.ajam.20130101.14
AB - In most of the literature in time series modeling, generalized autoregressive conditional heterosceasticity (GARCH) models has been used as a traditional model to forecast both the economic and financial time series data. Though literature has shown that it is not suitable for non-linear time series. For this reason, this model was augmented with bilinear model in order to make it more relevant in forecasting both economic and financial time series data. After the augmentation, the new model called Bilinear-GARCH (BL-GARCH) shows a better performance based on performance measures indices, models variances and out-of–samples forecast performances. In term of these three criteria the new models outperformed the traditional or classical GARCH model. To drive home this point, these two models were illustrated with Botswana inflation rates data. We observed that the new model (BL-GARCH) outperformed the classical GARCH model.
VL - 1
IS - 1
ER -

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Author Information

Akintunde Mutairu Oyewale

Department of Statistics, University of Botswana, Botswana
D. K. Shangodoyin

Department of Statistics, University of Botswana, Botswana
P. M Kgosi

Department of Statistics, University of Botswana, Botswana

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Plain Text BibTeX RIS

APA Style

Akintunde Mutairu Oyewale, D. K. Shangodoyin, P. M Kgosi. (2013). Measuring the Forecast Performance of GARCH and Bilinear-GARCH Models in Time Series Data. American Journal of Applied Mathematics, 1(1), 17-23. https://doi.org/10.11648/j.ajam.20130101.14

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ACS Style

Akintunde Mutairu Oyewale; D. K. Shangodoyin; P. M Kgosi. Measuring the Forecast Performance of GARCH and Bilinear-GARCH Models in Time Series Data. Am. J. Appl. Math. 2013, 1(1), 17-23. doi: 10.11648/j.ajam.20130101.14

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AMA Style

Akintunde Mutairu Oyewale, D. K. Shangodoyin, P. M Kgosi. Measuring the Forecast Performance of GARCH and Bilinear-GARCH Models in Time Series Data. Am J Appl Math. 2013;1(1):17-23. doi: 10.11648/j.ajam.20130101.14

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@article{10.11648/j.ajam.20130101.14,
  author = {Akintunde Mutairu Oyewale and D. K. Shangodoyin and P. M Kgosi},
  title = {Measuring the Forecast Performance of GARCH and Bilinear-GARCH Models in Time Series Data},
  journal = {American Journal of Applied Mathematics},
  volume = {1},
  number = {1},
  pages = {17-23},
  doi = {10.11648/j.ajam.20130101.14},
  url = {https://doi.org/10.11648/j.ajam.20130101.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20130101.14},
  abstract = {In most of the literature in time series modeling, generalized autoregressive conditional heterosceasticity (GARCH) models has been used as a traditional model to forecast both the economic and financial time series data. Though literature has shown that it is not suitable for non-linear time series. For this reason, this model was augmented with bilinear model in order to make it more relevant in forecasting both economic and financial time series data. After the augmentation, the new model called Bilinear-GARCH (BL-GARCH) shows a better performance based on performance measures indices, models variances and out-of–samples forecast performances. In term of these three criteria the new models outperformed the traditional or classical GARCH model. To drive home this point, these two models were illustrated with Botswana inflation rates data. We observed that the new model (BL-GARCH) outperformed the classical GARCH model.},
 year = {2013}
}

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