Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian

Teneng, Dean (2012): Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian.

Abstract

We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Kaarik and Umbleja (2011) proposed strategy. We observe that daily closing prices(12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF AND TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the otherway around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.

• Item Type: MPRA Paper
• Language: English
• Keywords: NIG, modeling, forecasting, foreign exchange, goodness of fits tests
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C46 - Specific Distributions ; Specific Statistics; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods

References

1. Barndorff–Nielsen O. E., Processes of normal inverse Gaussian type, Finance & Stochastics, 2, (1998), 42–68.

2. Figueroa-López J. E., Jump diffusion models driven by Lévy Processes, Springer Handbooks of Computational Statistics, (2012), 61–88.

3. Hauner D., Lee J. and Takizawa H., In Which Exchange Rate Models Do Forecasters Trust? ,IMF working paper WP/11/116, May 2010.

4. Käärik M., Umbleja M., On claim size fitting and rough estimation of risk premiums based on Estonian traffic example, International Journal of Mathematical Models and Methods in Applied Sciences, Issue 1, Vol. 5, 17–24, (2011).

5. Schoutens W., Lévy Processes in Finance, John Wiley & Sons Inc., New York, (2003).

6. D. Teneng, NIG-Lévy process in asset price modeling: Case of Estonian companies. In: RAMIK, J and STAVAREK, D. (eds.) Proceedings of the 30th International Conference on Mathematical Methods in Economics. Karvina: Silesian University, School of Business Administration, 2012, pg 891–896.

7. D. Teneng, Modeling foreign exchange closing prices with normal inverse Gaussian distribution. In: Lytvynenko, I. O., and Terletskyi, D. O. (eds.) Proceedings of the Second International Scientific Conference of Students and Young Scientists:Theoretical and Applied Aspects of Cybernetics. Kiev: Taras Shevchenko National University of Kiev, Cybernetics Faculty, 2012, pg 141–144.

8. D. Teneng and K. Pärna: Modeling and forcasting world indexes with normal inverse Gaussian. Proceedings of the 13th Symposium of Mathematics and its Applications: "Politehnica" University of Timisoara, November, 1-3, 2012, ISSN 1224-6069, page 303-305.

9. Rydberg T. H., The Normal Inverse Gaussian Lévy Process : Simulation and approximation, Comm. Stat.: Stoch. Models, Vol. 13 (4), 887–910, (1997).

10. http://en.wikipedia.org/wiki/Foreign_ exchange_market accessed 27/08/2012.