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Modelling the Volatility of Exchange Rates in Rwandese Markets

Received: 15 August 2014     Accepted: 19 March 2015     Published: 25 September 2015
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Abstract

This work applied Generalized Autoregressive Conditional Heteroskedasticity (GARCH) approachto modelling volatility in Rwanda Exchange rate returns. The Autoregressive (AR) model with GARCH errors was fitted to the daily exchange rate returns using Quasi-Maximum Likelihood Estimation (Q-MLE) method to get the current volatility, asymptotic consistency and asymptotic normality of estimated parameters.Akaike Information criterion was used for appropriate GARCH model selection while Jarque Bera test used for normality testing revealed that both returns and residuals have fat tails behaviour. It was shown that the estimated model fits Rwanda exchange rate returns data well.

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)
DOI 10.11648/j.ajtas.20150406.12
Page(s) 426-431
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), 2015. Published by Science Publishing Group

Keywords

Model, Volatility, ExchangeRate, Quasi Maximum Likelihood, GARCH Model

References
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[2] Blum, P., & Dacorogna, M. (2002). Extreme moves in daily Foreign Exchange rates and risk limit setting. . Department of Mathematics General Guisan Quasi Vol26 , , 8092Z'urich.
[3] Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroscedasticity . Journal of Econometris Vol.31 , 307-327.
[4] Engle, F. (19982). Autoregressive Conditional Heteroscedasticity with Estimates of Variance of United Kingdom Inflation. Econometrica Vol.50 , 987-1008.
[5] Franq, C., & Zakoian, J. (2004). Maximam Likelihood Estimationof Pure GARCH and ARMA-GARCH Processes . Bernoulli Vol.10 , 605-637.
[6] Ghysels, E., Harvey, A., & Renault, E. (1996). Stochastic Volatility. In Handbook of Statistics. Statistical Methods in Finance, Maddala, G.S. Ed. North- Holland, Amsterdam Vol.14 , 119-91.
[7] Glosten, L., Jagannathan, R., & Runkle, D. (1993). On the relation between the expected value and the Volatility of Nominal excess return on stocks. Journal of Finance Vol.48 , 1779-1801.
[8] Hull, J., & White, A. (1998). Value at Risk When Changes in Market Variables are not Normally Distributed. Journal of Risk Vol.1 , 47-61.
[9] Longin, F. (1996). The Asymptotic Distribution of Extreme Stock Market Returns . Journal of Business Vol.67 , 383-408.
[10] Maan, I., Mwita, N. P., & Odhiambo, R. (2010). Modelling the Volatility of Exchange Rates in the Kenyan Markets. Journal of Business Management Vol.4 , 1401-1408.
[11] Madura, J. (1989). International Financial Management 2nd Ed. St.Paul Minnesta: West Publishing Company.
[12] Manganelli, S., & Engle, R. (2001). Value at Risk Models in Finance,European Central Bank Working Paper Series, Frankfurt. Modelling. Mathematical Finance Vol.14 , 75-102.
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[14] Nelson, D. (1991). Conditional Heteroscedasticity in asset returns: A new Approach. Econometrica Vol.59 , 347-370.
[15] Posedel, P. (2005). Properties and Estimation of GARCH(1,1) Model . Metodolo S Ki Zvezki Vol.2 , 243-257.
[16] Sandmann, G., & Koopman, S. (1998). Estimation of Stochastics Volatility Models Via Monte Carlo Maximum Likelihood . Journal of Econometrics Vol.87 , 271-301.
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Cite This Article
  • APA Style

    Jean de Dieu Ntawihebasenga, Joseph Kyalor Mung’atu, Peter Nyamuhanga Mwita. (2015). Modelling the Volatility of Exchange Rates in Rwandese Markets. American Journal of Theoretical and Applied Statistics, 4(6), 426-431. https://doi.org/10.11648/j.ajtas.20150406.12

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    ACS Style

    Jean de Dieu Ntawihebasenga; Joseph Kyalor Mung’atu; Peter Nyamuhanga Mwita. Modelling the Volatility of Exchange Rates in Rwandese Markets. Am. J. Theor. Appl. Stat. 2015, 4(6), 426-431. doi: 10.11648/j.ajtas.20150406.12

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    AMA Style

    Jean de Dieu Ntawihebasenga, Joseph Kyalor Mung’atu, Peter Nyamuhanga Mwita. Modelling the Volatility of Exchange Rates in Rwandese Markets. Am J Theor Appl Stat. 2015;4(6):426-431. doi: 10.11648/j.ajtas.20150406.12

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  • @article{10.11648/j.ajtas.20150406.12,
      author = {Jean de Dieu Ntawihebasenga and Joseph Kyalor Mung’atu and Peter Nyamuhanga Mwita},
      title = {Modelling the Volatility of Exchange Rates in Rwandese Markets},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {4},
      number = {6},
      pages = {426-431},
      doi = {10.11648/j.ajtas.20150406.12},
      url = {https://doi.org/10.11648/j.ajtas.20150406.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.12},
      abstract = {This work applied Generalized Autoregressive Conditional Heteroskedasticity (GARCH) approachto modelling volatility in Rwanda Exchange rate returns. The Autoregressive (AR) model with GARCH errors was fitted to the daily exchange rate returns using Quasi-Maximum Likelihood Estimation (Q-MLE) method to get the current volatility, asymptotic consistency and asymptotic normality of estimated parameters.Akaike Information criterion was used for appropriate GARCH model selection while Jarque Bera test used for normality testing revealed that both returns and residuals have fat tails behaviour. It was shown that the estimated model fits Rwanda exchange rate returns data well.},
     year = {2015}
    }
    

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    T1  - Modelling the Volatility of Exchange Rates in Rwandese Markets
    AU  - Jean de Dieu Ntawihebasenga
    AU  - Joseph Kyalor Mung’atu
    AU  - Peter Nyamuhanga Mwita
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    DO  - 10.11648/j.ajtas.20150406.12
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
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    UR  - https://doi.org/10.11648/j.ajtas.20150406.12
    AB  - This work applied Generalized Autoregressive Conditional Heteroskedasticity (GARCH) approachto modelling volatility in Rwanda Exchange rate returns. The Autoregressive (AR) model with GARCH errors was fitted to the daily exchange rate returns using Quasi-Maximum Likelihood Estimation (Q-MLE) method to get the current volatility, asymptotic consistency and asymptotic normality of estimated parameters.Akaike Information criterion was used for appropriate GARCH model selection while Jarque Bera test used for normality testing revealed that both returns and residuals have fat tails behaviour. It was shown that the estimated model fits Rwanda exchange rate returns data well.
    VL  - 4
    IS  - 6
    ER  - 

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Author Information
  • Mahatma Gandhi University-Rwanda, Faculty of Science, Department of Mathematics, Kigali-Rwanda

  • Jomo Kenyatta University of Agriculture and Technology, Faculty of Applied Science, Department of Statistics and Actuarial Science, Kisumu-Kenya

  • Jomo Kenyatta University of Agriculture and Technology, Faculty of Applied Science, Department of Statistics and Actuarial Science, Nairobi-Kenya

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