Your browser does not support the PubReader view.
Go to this page to see a list of supporting browsers.
Seoul Journal of Economics
[ Article ]
Seoul Journal of Economics - Vol. 20, No. 2, pp.201-222
ISSN: 1225-0279 (Print)
Print publication date 31 May 2007
Received 27 Feb 2006 Revised 29 Dec 2006

Poisson Jumps and Long Memory Volatility Process in High Frequency European Exchange Rates

Young Wook Han
Assistant Professor, Department of Economics, Hallym University, Chuncheon, Gangwon-Do 200-702, Korea, Tel: +82-33-248-1820, Fax: +82-33-256-3424 ywhan@hallym.ac.kr

JEL Classification: C13, C22, F31, G14

Abstract

This paper analyzes the intriguing features of 30-minute European foreign exchange rates during the year 1996; jumps and long memory volatility process. The FIGARCH model with the Poisson distribution is applied in order to consider both the jumps in the conditional mean process and the long memory property in the conditional variance process of the high frequency foreign exchange returns series. The general results show that the Poisson distribution accounts for the jumps in the high frequency foreign exchange rates returns quite well and that the jumps seem to spuriously induce higher long memory property in the high frequency foreign exchange returns. Hence, the FIGARCH model with the Poisson distribution appears to be quite appropriate for the specification of the high frequency returns.

Keywords:

High frequency foreign exchange rates, FIGARCH, Long memory property, Normal mixture distribution, Poisson jump process

Acknowledgments

I am very grateful to the Editor, In Ho Lee and two anonymous referees for useful comments and suggestions and gratefully acknowledge the financial support from Hallym University Research Fund (HRF 2005). I also thank Olsen and Associates and MMS (Money Market Service) International for making available the high frequency exchange rate data and the public macroeconomic news of the US and Germany during 1996.

References

  • Akgiray, V., and Booth, G. G. “Mixed Diffusion-Jump Process Modeling of Exchange Rate Movements.” Review of Economics and Statistics 70 (No. 4 1988): 631-7. [https://doi.org/10.2307/1935826]
  • Andersen, Torben G., and Bollerslev, Tim. “Intraday Periodicity and Volatility Persistence in Financial Markets.” Journal of Empirical Finance 4 (Nos. 2-3 1997): 115-58. [https://doi.org/10.1016/S0927-5398(97)00004-2]
  • Andersen, Torben G., and Bollerslev, Tim. “Deutsche Mark - Dollar Volatility: Intraday Activity, Patterns, Macroeconomic Announcements and Longer Run Dependence.” Journal of Finance 53 (No. 1 1998): 219-65. [https://doi.org/10.1111/0022-1082.85732]
  • Andersen, Torben G., Bollerslev, Tim, Diebold, Francis X., and Vega, Clara. “Micro Effects of Macro Announcements: Real-time Price Discovery in Foreign Exchange.” American Economic Reviews 93 (No. 1 2003): 38-62. [https://doi.org/10.1257/000282803321455151]
  • Baillie, R. T. “Long Memory Processes and Fractional Integration in Econometrics.” Journal of Econometrics 73 (No. 1 1996): 5-59. [https://doi.org/10.1016/0304-4076(95)01732-1]
  • Baillie, Richard T., and Bollerslev, Tim. “Intra-day and Inter-market Volatility in Foreign Exchange Rates.” Review of Economic Studies 58 (No. 3 1991): 565-85. [https://doi.org/10.2307/2298012]
  • Baillie, Richard T., Bollerslev, Tim, and Mikkelsen, Hans O. “Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics 74 (No. 1 1996): 3-30. [https://doi.org/10.1016/S0304-4076(95)01749-6]
  • Baillie, Richard T., Cecen, Aydin A., Erkal, Cahit, and Han, Young W. “Merging the Stochastic with the Nonlinear Deterministic: the Case of High Frequency European Exchange Rates.” Journal of International Financial Markets, Institutions and Money 14 (No. 5 2004): 401-18. [https://doi.org/10.1016/j.intfin.2003.12.002]
  • Baillie, Richard T., Cecen, Aydin C., and Han, Young W. “High Frequency Deutschemark - US Dollar Returns: FIGARCH Representations and Non Linearities.” Multinational Finance Journal 4 (Nos. 3-4 2000): 247-67. [https://doi.org/10.17578/4-3/4-6]
  • Baillie, Richard. T., and Han, Young W. “Comment on Testing Target Zone Models Using Efficient Methods of Moments.” Journal of Business and Economic Statistics 19 (No. 3 2001): 273-7. [https://doi.org/10.1198/073500101681019891]
  • Ball, Clifford, and Roma, Antoni. “A Jump Diffusion Model for the European Monetary System.” Journal of International Money and Finance 12 (No. 5 1993): 475-92. [https://doi.org/10.1016/0261-5606(93)90035-A]
  • Ball, Clifford, and Torous, Walter. “A Simplified Jump Process for Common Stock Returns.” Journal of Financial and Quantitative Analysis 18 (No. 1 1983): 53-65. [https://doi.org/10.2307/2330804]
  • Beine, Michel, Benassy-Quere, Agnes, and Lecourt, Chrstelle. “Central Bank Intervention and Foreign Exchange Rate: New Evidence from FIGARCH Estimations.” Journal of International Money and Finance 21 (No. 1 2002a): 115-44. [https://doi.org/10.1016/S0261-5606(01)00040-7]
  • Beine, Michel, and Laurent, Sebastien. “Structural Change and Long Memory in Volatility: New Evidence from Daily Exchange Rates.” In C. Dunis, A. Timmerman, and J. Moody (eds.), Developments in Forest Combination and Portfolio Choice, Wiley Series in Quantitative Analysis, Wiley: London, 2001.
  • Beine, Michel, and Laurent, Sebastien. “Central Bank Interventions and Jumps in Double Long Memory Models of Daily Exchange Rates.” Journal of Empirical Finance 10 (No. 5 2003): 641-60. [https://doi.org/10.1016/S0927-5398(03)00009-4]
  • Beine, Michel, Laurent, Sebastien, and Lecourt, Christelle. “Account for Conditional Leptokurtosis and Closing Days Effects in FIGARCH Models of Daily Exchange Rates.” Applied Financial Economics 12 (No. 8 2002b): 589-600. [https://doi.org/10.1080/09603100010014041]
  • Beltratti, Andrea, and Morana, Claudio. “Computing Value at Risk with High Frequency Data.” Journal of Empirical Finance 6 (No. 5 1999): 431-55. [https://doi.org/10.1016/S0927-5398(99)00008-0]
  • Bollerslev, T. “Generalized Autoregressive Conditional Heteroscedasticity.” Journal of Econometrics 31 (No. 3 1986): 307-27. [https://doi.org/10.1016/0304-4076(86)90063-1]
  • Bollerslev, Tim, and Wooldridge, Jeff M. “Quasi-maximum Likelihood Estimation of Dynamic Models with Time Varying Covariances.” Econometric Reviews 11 (No. 2 1992): 143-72. [https://doi.org/10.1080/07474939208800229]
  • Cheung, Chae-Shik, and Tauchen, George. “Testing Target Zone Models Using Efficient Methods of Moments.” Journal of Business and Economic Statistics 19 (No. 3 2001): 276-7. [https://doi.org/10.1198/073500101681019891]
  • Covrig, Vicentiu, and Melvin, Michael T. “Asymmetric Information and Price Discovery in the FX Market: Does Tokyo Know More about Yen?” Journal of Empirical Finance 9 (No. 3 2002): 271-85. [https://doi.org/10.1016/S0927-5398(01)00056-1]
  • Dacorogna, Michel M., Müller, Ulrich A., Nagler, Rob J., Olsen, Richarrd B., and Pictet, Olivier V. “A Geographical Model for Daily and Weekly Seasonal Volatility in the Foreign Exchange Markets.” Journal of International Money and Finance 12 (No. 4 1993): 413-38. [https://doi.org/10.1016/0261-5606(93)90004-U]
  • Diebold, F. X. “Empirical Modeling of Exchange Rate Dynamics. Lecture Notes in Economics and Mathematical Systems.” Series, No. 303, New York: Springer, 1988. [https://doi.org/10.1007/978-3-642-45641-1]
  • Diebold, F. X., and Inoue, A. Long Memory and Structural Change. Manuscript, Department of Finance, Stern School, NYU, 1999.
  • Gallant, Ronald. “On the Bias in Flexible Function Forms and an Essentially Unbiased Form: The Fourier Flexible Form.” Journal of Econometrics 15 (No. 2 1981): 211-45. [https://doi.org/10.1016/0304-4076(81)90115-9]
  • Gallant, Ronald. “Unbiased Determination of Production Technologies.” Journal of Econometrics 20 (No. 2 1982): 285-323. [https://doi.org/10.1016/0304-4076(82)90022-7]
  • Ghosh, Dillip. “Negative Autocorrelation around Large Jumps in Intra-day Foreign Exchange Data.” Economic Letters 56 (No. 2 1997): 235-41. [https://doi.org/10.1016/S0165-1765(97)81906-4]
  • Goodhart, Charles A. E., and Figliuoli, Lorenzo. “Every Minute Counts in Financial Markets.” Journal of International Money and Finance 10 (No. 1 1992): 23-52. [https://doi.org/10.1016/0261-5606(91)90025-F]
  • Goodhart, Charles A. E., and Giugale, Marcelo. “From Hour to Hour in the Foreign Exchange Market.” The Manchester School, LXI (No. 1 1993): 1-34. [https://doi.org/10.1111/j.1467-9957.1993.tb00222.x]
  • Goodhart, Charles A. E., Hall, Stephen G., Henry, Brian S., and Pesaran, Bahram. “News Effects in a High Frequency Model of the Sterling-Dollar Exchange Rate.” Journal of Applied Econometrics 8 (No. 1 1993): 1-13. [https://doi.org/10.1002/jae.3950080102]
  • Goodhart, C. A. E., and O'Hara, M. “High Frequency Data in Financial Markets: Issues and Applications.” Journal of Empirical Finance 4 (Nos. 2-3 1997): 73-114. [https://doi.org/10.1016/S0927-5398(97)00003-0]
  • Granger, C. W. J. “Long Memory Relationships and the Aggregation of Dynamic Models.” Journal of Econometrics 14 (No. 2 1980): 227-38. [https://doi.org/10.1016/0304-4076(80)90092-5]
  • Granger, Clive W. J., and Ding, Zuanxin. “Some Properties of Absolute Returns: An Alternative Measure of Risk.” Annales d'Economie et de Statistique 40 (No. 1 1995): 67-92. [https://doi.org/10.2307/20076016]
  • Granger, Clive W. J., and Hyung, Namwon. “Occasional Structural Breaks and Long Memory with an Application to the S&P500 Absolute Stock Returns.” Journal of Empirical Finance 11 (No. 3 2004): 399-421. [https://doi.org/10.1016/j.jempfin.2003.03.001]
  • Granger, C. W. J., and Joyeux, R. “An Introduction to Long Memory Time Series Models and Fractional Differencing.” Journal of Time Series Analysis 1 (No. 1 1980): 15-39. [https://doi.org/10.1111/j.1467-9892.1980.tb00297.x]
  • Han, Y. W. “High Frequency Perspective on Jump Process, Long Memory Property and Temporal Aggregation: Case of $-Aud Exchange Rates.” Journal of Japan and the World Economy 19 (No.7 2007): 248-62. [https://doi.org/10.1016/j.japwor.2006.01.001]
  • Hosking, J. R. M. “Fractional Differencing.” Biometrika 68 (No. 1 1981): 165-76. [https://doi.org/10.1093/biomet/68.1.165]
  • Hotta, Luiz K., and Tsay, Ruley S. Outliers in GARCH Process. Unpublished Manuscript, 1998.
  • Hsieh, D. A. “Testing for Nonlinear Dependence in Daily Foreign Exchange Rates.” Journal of Business 62 (No. 3 1989): 339-68. [https://doi.org/10.1086/296466]
  • Jorion, Phillippe. “On Jump Processes in the Foreign Exchange and Stock Markets.” Review of Financial Studies 1 (No. 4 1988): 427-45. [https://doi.org/10.1093/rfs/1.4.427]
  • Müller, Ulrich A., Dacorogna, Michel M., Olsen, Richard B., Pictet, Olivier V., Schwarz, Michel, and Morgenegg, Claudio. “Statistical Study of Foreign Exchange Rates, Empirical Evidence of Price Change Law, and Intraday Analysis.” Journal of Banking and Finance 14 (No. 6 1990): 1189-208. [https://doi.org/10.1016/0378-4266(90)90009-Q]
  • Neely, Christoper. “Target Zones and Conditional Volatility: The Role of Realignments.” Journal of Empirical Finance 6 (No. 2 1999): 177-92. [https://doi.org/10.1016/S0927-5398(98)00015-2]
  • Nieuwland, Fred, Verschoor, William, and Wolff, Christan C. P. “EMS Exchange Rates.” Journal of International Financial Markets, Institutions and Money 2 (No. 1 1991): 21-42.
  • Nieuwland, Fred, Verschoor, William, and Wolff, Christan C. P. “Stochastic Trends and Jumps in EMS Exchange Rates.” Journal of International Money and Finance 13 (No. 6 1994): 699-727. [https://doi.org/10.1016/0261-5606(94)90039-6]
  • Press, James. “A Compound Events Model for Security Prices.” Journal of Business 40 (No. 2 1967): 317-35. [https://doi.org/10.1086/294980]
  • Vlaar, P. J. G., and Palm, F. “The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion, Conditional Heteroskedasticity and Jumps.” Journal of Business and Economic Statistics 11 (No. 3 1993): 351-60. [https://doi.org/10.1080/07350015.1993.10509963]
  • Vlaar, P. J. G., and Palm, F. “Inflation Differentials and Excess Returns in the European Monetary System.” Journal of International Financial Markets, Institutions and Money 7 (No. 1 1997): 1-20. [https://doi.org/10.1016/S1042-4431(97)00008-5]
  • Wasserfallen, Walter. “Flexible Exchange Rates: A Closer Look.” Journal of Monetary Economics 23 (No. 3 1989): 511-21. [https://doi.org/10.1016/0304-3932(89)90044-5]
  • Zhou, B. “High Frequency Data and Volatility in Foreign Exchange Rates.” Journal of Business and Economic Statistics 14 (No. 1 1996): 45-52. [https://doi.org/10.1080/07350015.1996.10524628]