Volatility of Some Selected Currencies Against the Naira Using Generalized Autoregressive Score Models

Oluwagbenga Tobi Babatunde; Henrietta Ebele Oranye; Cynthia Ndidiamaka Nwafor

doi:doi:10.11648/j.ijsd.20200603.11

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Volatility of Some Selected Currencies Against the Naira Using Generalized Autoregressive Score Models

Oluwagbenga Tobi Babatunde, Henrietta Ebele Oranye, Cynthia Ndidiamaka Nwafor

Published in International Journal of Statistical Distributions and Applications (Volume 6, Issue 3)

Received: 20 July 2020 Accepted: 30 July 2020 Published: 27 August 2020

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Abstract

The role exchange rate plays in international trade and bilateral agreement between countries cannot be over-emphasize. Fluctuations in exchange rate has direct impact on the economy of any country especially a country like Nigeria which depends largely on import goods. So, there is need to identify appropriate model that can adequately describe the dynamics of the exchange rate volatilities. This article investigated the volatility of exchange rates in Nigeria by selecting the U.S dollars, Pound Sterling and Euro against the Naira using daily data over the period of January 02, 2002 to August 31, 2018. The GAS model with its variants was applied to study the volatility of the exchange rates assuming three different probability distributions for the innovations of the models namely; Normal distribution (N), Student-t distribution (T) and Skewed-Student-t distribution (SKT). The AIC and SBIC estimates obtained were used to access fitness performance. The GAS model and its variants’ forecasting ability were access using several forecast measures. Using the estimates of the AIC and SBIC, GAS-T, EGAS-T and EGAS-STK were selected for US dollars/Naira, Pound sterling/Naira and Euro/Naira exchange rates respectively as the best fitted models. Based on the estimates of MAE and RMSE, GAS-T, EGAS-T and EGAS-SKT were selected for forecasting the volatility of US dollars/Naira, Pound sterling/Naira and Euro/Naira exchange rates respectively.

Published in	International Journal of Statistical Distributions and Applications (Volume 6, Issue 3)
DOI	10.11648/j.ijsd.20200603.11
Page(s)	42-46
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

Volatility, Generalized Autoregressive Score, Exchange Rates, Innovations

References

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[3]	Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics 31: 307–27.
[4]	Nelson, D. B. (1991). Conditional Heteroscedasticity in Asset Returns: A New Approach. Econometrica, 59, 347–370.
[5]	Glosten, L. W., Jaganathan, R. and Runkle, D. E. (1993). “On the relation between the expected value and the volatility of the nominal excess return on stocks”. Journal of Finance 48: 1779–1801.
[6]	Ding, Z., Granger, C. W. J. and Engle, R. F. (1993). “A long memory property of stock market returns and a new model”. Journal of Empirical Finance, 1: 83-106.
[7]	Gonzalez-Rivera, G. (1998). Smooth transition GARCH models. Studies in Nonlinear Dynamics and Econometrics 3, 61-78.
[8]	Yaya, O. S., Bada, V. and Atoi, N. V. (2016). Volatility in the Nigerian Stock Market: Emperical Application of Beta-t-GARCH Variants. CBN Journal of Applied Statistics, 7, 27-48.
[9]	Harvey, A. and Chakravarty, T. (2008). Beta-t-(E)GARCH. Working paper series. University of Cambridge.
[10]	Harvey, A. (2013). Dynamic Models for volatility and Heavy tails: with applications to financial and economic time series. Cambridge University Press, London.
[11]	Blasques, F., Koopman, S. J. and Lucas, A. (2008). Stationarity and Ergodicity of Univariate GAS Process. Electronic Journal of Statistics. Vol. 8, pp. 1088-1112.
[12]	Creal, D., Koopman, S. J., and Lucas, A. (2013). Generalized autoregressive score models with applications. Journal of Applied Econometrics, 28 (5): 777-795.
[13]	Calvori, F., Cipollini, F. and Gallo, G. M. (2013). Go with the flow: A GAS Model for Predicting Intra-daily Volume Shares. Social Science Research Network. http://ssrn.com/abstract=2363483.
[14]	Huang, Z., Wang, T. and Zhang, X. (2014). GAS model with realized measures of volatility. http://ssrn.com/abstract=2461831.
[15]	Blasques, F., Koopman, S. J. and Lucas, A. (2014). Maximum Likelihood Estimation for GAS models. Tinbergen Institute Discussion Paper 14-029/III.
[16]	Janus, P., Lucas, A. and Opschoor, A. (2014). New Heavy Models for FatTailed Returns and Realized Covariance Kernels. Tinbergen Institute Discussion Paper 14-073/IV.
[17]	Bernadi, M. and Cantania, L. (2015). Switching-GAS copula models for systemic Risk Assessment. arxiv.org/abs/1504.03733vi.
[18]	Babatunde, O. T., Yaya, O. S. and Oladugba, A., V. (2020). Investigating the Specification of the Distributional Assumption of the Innovations of Generalised Autoregressive Score Model with its Variants. International Journal of Applied Mathematics and Statistics, 59 (4).
[19]	Babatunde, O. T., Yaya, O. S and Akinlana, D. M. (2019). Misspecification of Generalized Autoregressive Score Models: Monte Carlo Simulations and Applications. International Journal of Mathematics Trends and Technology, 65 (3).

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APA Style

Oluwagbenga Tobi Babatunde, Henrietta Ebele Oranye, Cynthia Ndidiamaka Nwafor. (2020). Volatility of Some Selected Currencies Against the Naira Using Generalized Autoregressive Score Models. International Journal of Statistical Distributions and Applications, 6(3), 42-46. https://doi.org/10.11648/j.ijsd.20200603.11

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ACS Style

Oluwagbenga Tobi Babatunde; Henrietta Ebele Oranye; Cynthia Ndidiamaka Nwafor. Volatility of Some Selected Currencies Against the Naira Using Generalized Autoregressive Score Models. Int. J. Stat. Distrib. Appl. 2020, 6(3), 42-46. doi: 10.11648/j.ijsd.20200603.11

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AMA Style

Oluwagbenga Tobi Babatunde, Henrietta Ebele Oranye, Cynthia Ndidiamaka Nwafor. Volatility of Some Selected Currencies Against the Naira Using Generalized Autoregressive Score Models. Int J Stat Distrib Appl. 2020;6(3):42-46. doi: 10.11648/j.ijsd.20200603.11

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@article{10.11648/j.ijsd.20200603.11,
  author = {Oluwagbenga Tobi Babatunde and Henrietta Ebele Oranye and Cynthia Ndidiamaka Nwafor},
  title = {Volatility of Some Selected Currencies Against the Naira Using Generalized Autoregressive Score Models},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {6},
  number = {3},
  pages = {42-46},
  doi = {10.11648/j.ijsd.20200603.11},
  url = {https://doi.org/10.11648/j.ijsd.20200603.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20200603.11},
  abstract = {The role exchange rate plays in international trade and bilateral agreement between countries cannot be over-emphasize. Fluctuations in exchange rate has direct impact on the economy of any country especially a country like Nigeria which depends largely on import goods. So, there is need to identify appropriate model that can adequately describe the dynamics of the exchange rate volatilities. This article investigated the volatility of exchange rates in Nigeria by selecting the U.S dollars, Pound Sterling and Euro against the Naira using daily data over the period of January 02, 2002 to August 31, 2018. The GAS model with its variants was applied to study the volatility of the exchange rates assuming three different probability distributions for the innovations of the models namely; Normal distribution (N), Student-t distribution (T) and Skewed-Student-t distribution (SKT). The AIC and SBIC estimates obtained were used to access fitness performance. The GAS model and its variants’ forecasting ability were access using several forecast measures. Using the estimates of the AIC and SBIC, GAS-T, EGAS-T and EGAS-STK were selected for US dollars/Naira, Pound sterling/Naira and Euro/Naira exchange rates respectively as the best fitted models. Based on the estimates of MAE and RMSE, GAS-T, EGAS-T and EGAS-SKT were selected for forecasting the volatility of US dollars/Naira, Pound sterling/Naira and Euro/Naira exchange rates respectively.},
 year = {2020}
}

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TY  - JOUR
T1  - Volatility of Some Selected Currencies Against the Naira Using Generalized Autoregressive Score Models
AU  - Oluwagbenga Tobi Babatunde
AU  - Henrietta Ebele Oranye
AU  - Cynthia Ndidiamaka Nwafor
Y1  - 2020/08/27
PY  - 2020
N1  - https://doi.org/10.11648/j.ijsd.20200603.11
DO  - 10.11648/j.ijsd.20200603.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 42
EP  - 46
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20200603.11
AB  - The role exchange rate plays in international trade and bilateral agreement between countries cannot be over-emphasize. Fluctuations in exchange rate has direct impact on the economy of any country especially a country like Nigeria which depends largely on import goods. So, there is need to identify appropriate model that can adequately describe the dynamics of the exchange rate volatilities. This article investigated the volatility of exchange rates in Nigeria by selecting the U.S dollars, Pound Sterling and Euro against the Naira using daily data over the period of January 02, 2002 to August 31, 2018. The GAS model with its variants was applied to study the volatility of the exchange rates assuming three different probability distributions for the innovations of the models namely; Normal distribution (N), Student-t distribution (T) and Skewed-Student-t distribution (SKT). The AIC and SBIC estimates obtained were used to access fitness performance. The GAS model and its variants’ forecasting ability were access using several forecast measures. Using the estimates of the AIC and SBIC, GAS-T, EGAS-T and EGAS-STK were selected for US dollars/Naira, Pound sterling/Naira and Euro/Naira exchange rates respectively as the best fitted models. Based on the estimates of MAE and RMSE, GAS-T, EGAS-T and EGAS-SKT were selected for forecasting the volatility of US dollars/Naira, Pound sterling/Naira and Euro/Naira exchange rates respectively.
VL  - 6
IS  - 3
ER  -

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Author Information

Oluwagbenga Tobi Babatunde

Department of Statistics, Faculty of Physical Sciences, University of Nigeria, Nsukka, Nigeria
Henrietta Ebele Oranye

Department of Statistics, Faculty of Physical Sciences, University of Nigeria, Nsukka, Nigeria
Cynthia Ndidiamaka Nwafor

Department of Statistics, Faculty of Physical Sciences, University of Nigeria, Nsukka, Nigeria

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APA Style

Oluwagbenga Tobi Babatunde, Henrietta Ebele Oranye, Cynthia Ndidiamaka Nwafor. (2020). Volatility of Some Selected Currencies Against the Naira Using Generalized Autoregressive Score Models. International Journal of Statistical Distributions and Applications, 6(3), 42-46. https://doi.org/10.11648/j.ijsd.20200603.11

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ACS Style

Oluwagbenga Tobi Babatunde; Henrietta Ebele Oranye; Cynthia Ndidiamaka Nwafor. Volatility of Some Selected Currencies Against the Naira Using Generalized Autoregressive Score Models. Int. J. Stat. Distrib. Appl. 2020, 6(3), 42-46. doi: 10.11648/j.ijsd.20200603.11

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AMA Style

Oluwagbenga Tobi Babatunde, Henrietta Ebele Oranye, Cynthia Ndidiamaka Nwafor. Volatility of Some Selected Currencies Against the Naira Using Generalized Autoregressive Score Models. Int J Stat Distrib Appl. 2020;6(3):42-46. doi: 10.11648/j.ijsd.20200603.11

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@article{10.11648/j.ijsd.20200603.11,
  author = {Oluwagbenga Tobi Babatunde and Henrietta Ebele Oranye and Cynthia Ndidiamaka Nwafor},
  title = {Volatility of Some Selected Currencies Against the Naira Using Generalized Autoregressive Score Models},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {6},
  number = {3},
  pages = {42-46},
  doi = {10.11648/j.ijsd.20200603.11},
  url = {https://doi.org/10.11648/j.ijsd.20200603.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20200603.11},
  abstract = {The role exchange rate plays in international trade and bilateral agreement between countries cannot be over-emphasize. Fluctuations in exchange rate has direct impact on the economy of any country especially a country like Nigeria which depends largely on import goods. So, there is need to identify appropriate model that can adequately describe the dynamics of the exchange rate volatilities. This article investigated the volatility of exchange rates in Nigeria by selecting the U.S dollars, Pound Sterling and Euro against the Naira using daily data over the period of January 02, 2002 to August 31, 2018. The GAS model with its variants was applied to study the volatility of the exchange rates assuming three different probability distributions for the innovations of the models namely; Normal distribution (N), Student-t distribution (T) and Skewed-Student-t distribution (SKT). The AIC and SBIC estimates obtained were used to access fitness performance. The GAS model and its variants’ forecasting ability were access using several forecast measures. Using the estimates of the AIC and SBIC, GAS-T, EGAS-T and EGAS-STK were selected for US dollars/Naira, Pound sterling/Naira and Euro/Naira exchange rates respectively as the best fitted models. Based on the estimates of MAE and RMSE, GAS-T, EGAS-T and EGAS-SKT were selected for forecasting the volatility of US dollars/Naira, Pound sterling/Naira and Euro/Naira exchange rates respectively.},
 year = {2020}
}

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TY  - JOUR
T1  - Volatility of Some Selected Currencies Against the Naira Using Generalized Autoregressive Score Models
AU  - Oluwagbenga Tobi Babatunde
AU  - Henrietta Ebele Oranye
AU  - Cynthia Ndidiamaka Nwafor
Y1  - 2020/08/27
PY  - 2020
N1  - https://doi.org/10.11648/j.ijsd.20200603.11
DO  - 10.11648/j.ijsd.20200603.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 42
EP  - 46
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20200603.11
AB  - The role exchange rate plays in international trade and bilateral agreement between countries cannot be over-emphasize. Fluctuations in exchange rate has direct impact on the economy of any country especially a country like Nigeria which depends largely on import goods. So, there is need to identify appropriate model that can adequately describe the dynamics of the exchange rate volatilities. This article investigated the volatility of exchange rates in Nigeria by selecting the U.S dollars, Pound Sterling and Euro against the Naira using daily data over the period of January 02, 2002 to August 31, 2018. The GAS model with its variants was applied to study the volatility of the exchange rates assuming three different probability distributions for the innovations of the models namely; Normal distribution (N), Student-t distribution (T) and Skewed-Student-t distribution (SKT). The AIC and SBIC estimates obtained were used to access fitness performance. The GAS model and its variants’ forecasting ability were access using several forecast measures. Using the estimates of the AIC and SBIC, GAS-T, EGAS-T and EGAS-STK were selected for US dollars/Naira, Pound sterling/Naira and Euro/Naira exchange rates respectively as the best fitted models. Based on the estimates of MAE and RMSE, GAS-T, EGAS-T and EGAS-SKT were selected for forecasting the volatility of US dollars/Naira, Pound sterling/Naira and Euro/Naira exchange rates respectively.
VL  - 6
IS  - 3
ER  -

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