IDEAS home Printed from https://ideas.repec.org/p/isu/genstf/1997010108000012997.html
   My bibliography  Save this paper

Statistical analysis of foreign exchange rates: application of cointegration model and regime-switching stochastic volatility model

Author

Listed:
  • Kondo, Koji

Abstract

The dissertation discusses an application of two statistical models to foreign exchange rate data and consists of two main parts. The first part is an application of the partial cointegration model developed by Johansen (1990) and uses the concept of weak exogeneity. While a direct application of the cointegration approach with many variables is not easy to handle, the partial model can reduce the number of the parameters to be estimated by identifying weakly exogenous variables. The method is illustrated utilizing a theoretical long-run model based on Dornbusch's sticky price model. The small country assumption is relaxed to that both countries are taken to be large. Furthermore the model is also extended to include a third country. The data set consists of monthly exchange rates, countries' money supplies, and GNPs. The three countries are Germany, Japan and the United States, thus giving a total of eight equations to be estimated. Three variables out of eight are identified as weakly exogenous variables and only five questions are estimated. Results show that there exist three cointegrating relations among the variables. One relation can be interpreted as long-run money market equilibrium while the other two relations, though considered to be long-run in nature, can not be interpreted in an economically meaningful way. Variance decomposition and impulse response analysis are conducted to investigate the dynamic of the system;In the second part of the dissertation a regime-switching stochastic volatility (RSV) model is applied to daily exchange rate data. The model is used to capture possible changing volatility of the exchange rate over time. The RSV model recommends itself since it is the more natural method to apply, as opposed to using ARCH and GARCH models. The main drawback however, is that it is the more complicated to implement. A Markov chain technique is used as an estimation method. By imposing interest rate parity, the relationship between exchange rate and foreign and domestic interest rate difference is also simultaneously examined. The results indicate that interest rate difference does not affect the level and the volatility of exchange rates. This finding supports the random walk theory of exchange rates. On the other hand two different regimes, a high-volatility regime and a low-volatility regime, are discovered and well modeled. The development of a forecasting model will be the subject for future studies.

Suggested Citation

  • Kondo, Koji, 1997. "Statistical analysis of foreign exchange rates: application of cointegration model and regime-switching stochastic volatility model," ISU General Staff Papers 1997010108000012997, Iowa State University, Department of Economics.
    • Handle: RePEc:isu:genstf:1997010108000012997
    as

    Download full text from publisher

    File URL: https://dr.lib.iastate.edu/server/api/core/bitstreams/f8a851ef-2cdf-4812-acdb-4ee2b8cbe5ca/content
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. McKinnon, Ronald I, 1982. "Currency Substitution and Instability in the World Dollar Standard," American Economic Review, American Economic Association, vol. 72(3), pages 320-333, June.
    2. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
    3. Christopher A. Sims, 1986. "Are forecasting models usable for policy analysis?," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 10(Win), pages 2-16.
    4. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220, National Bureau of Economic Research, Inc.
    5. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    6. Richard Meese & Kenneth Rogoff, 1983. "The Out-of-Sample Failure of Empirical Exchange Rate Models: Sampling Error or Misspecification?," NBER Chapters, in: Exchange Rates and International Macroeconomics, pages 67-112, National Bureau of Economic Research, Inc.
    7. Baillie, Richard T. & Selover, David D., 1987. "Cointegration and models of exchange rate determination," International Journal of Forecasting, Elsevier, vol. 3(1), pages 43-51.
    8. Hossain, Ferdaus, 1995. "Current account determination in the intertemporal framework: an empirical analysis," ISU General Staff Papers 1995010108000011939, Iowa State University, Department of Economics.
    9. Andrew A. Weiss, 1984. "Arma Models With Arch Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 5(2), pages 129-143, March.
    10. Urbain, Jean-Pierre, 1992. "On Weak Exogeneity in Error Correction Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(2), pages 187-207, May.
    11. Dibooglu, Selahattin, 1993. "Multiple cointegration and structural models: applications to exchange rate determination," ISU General Staff Papers 1993010108000011419, Iowa State University, Department of Economics.
    12. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    13. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    14. Ronald Mahieu & Peter C. Schotman, 1994. "Stochastic volatility and the distribution of exchange rate news," Discussion Paper / Institute for Empirical Macroeconomics 96, Federal Reserve Bank of Minneapolis.
    15. Johansen, Soren, 1992. "Cointegration in partial systems and the efficiency of single-equation analysis," Journal of Econometrics, Elsevier, vol. 52(3), pages 389-402, June.
    16. Calvo, Guillermo A & Rodriguez, Carlos Alfredo, 1977. "A Model of Exchange Rate Determination under Currency Substitution and Rational Expectations," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 617-625, June.
    17. Frankel, Jeffrey A, 1979. "On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differentials," American Economic Review, American Economic Association, vol. 69(4), pages 610-622, September.
    18. Mahieu, Ronald & Schotman, Peter, 1994. "Neglected common factors in exchange rate volatility," Journal of Empirical Finance, Elsevier, vol. 1(3-4), pages 279-311, July.
    19. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    20. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    21. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
    22. Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665, National Bureau of Economic Research, Inc.
    23. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    24. Hatanaka, Michio, 1996. "Time-Series-Based Econometrics: Unit Roots and Co-integrations," OUP Catalogue, Oxford University Press, number 9780198773535, Decembrie.
    25. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
    26. Olivier J. Blanchard & Mark W. Watson, 1986. "Are Business Cycles All Alike?," NBER Chapters, in: The American Business Cycle: Continuity and Change, pages 123-180, National Bureau of Economic Research, Inc.
    27. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
    28. Rudiger Dornbusch, 1980. "Exchange Rate Economics: Where Do We Stand?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 11(1, Tenth ), pages 143-206.
    29. Daniel B. Nelson, 1994. "Asymptotically Optimal Smoothing with ARCH Models," NBER Technical Working Papers 0161, National Bureau of Economic Research, Inc.
    30. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-840, September.
    31. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    32. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
    33. Ruiz, Esther, 1994. "Quasi-maximum likelihood estimation of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 63(1), pages 289-306, July.
    34. Frenkel, Jacob A. & Rodriguez, Carlos A., 1980. "Exchange Rate Dynamics and Overshooting Hypothesis," Foerder Institute for Economic Research Working Papers 275323, Tel-Aviv University > Foerder Institute for Economic Research.
    35. Kouri, Pentti J K, 1976. " The Exchange Rate and the Balance of Payments in the Short Run and in the Long Run: A Monetary Approach," Scandinavian Journal of Economics, Wiley Blackwell, vol. 78(2), pages 280-304.
    36. Mussa, Michael, 1976. " The Exchange Rate, the Balance of Payments and Monetary and Fiscal Policy under a Regime of Controlled Floating," Scandinavian Journal of Economics, Wiley Blackwell, vol. 78(2), pages 229-248.
    37. John F. O. Bilson & Richard C. Marston, 1984. "Exchange Rate Theory and Practice," NBER Books, National Bureau of Economic Research, Inc, number bils84-1, March.
    38. Frenkel, Jacob A. & Mussa, Michael L., 1985. "Asset markets, exchange rates and the balance of payments," Handbook of International Economics, in: R. W. Jones & P. B. Kenen (ed.), Handbook of International Economics, edition 1, volume 2, chapter 14, pages 679-747, Elsevier.
    39. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    40. Hsieh, David A, 1989. "Modeling Heteroscedasticity in Daily Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 307-317, July.
    41. Hendry, David F., 1995. "Dynamic Econometrics," OUP Catalogue, Oxford University Press, number 9780198283164, Decembrie.
    42. Carriquiry, Alicia L. & Breidt, F. J., 1996. "Improved Quasi-Maximum Likelihood for Stochastic Volatility Models," Staff General Research Papers Archive 1035, Iowa State University, Department of Economics.
    43. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    44. Ruiz Ortega, Esther, 1993. "Stochastic volatility versus autoregressive conditional heteroscedasticity," DES - Working Papers. Statistics and Econometrics. WS 5708, Universidad Carlos III de Madrid. Departamento de Estadística.
    45. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    46. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    47. Pentti J.K. Kouri & Jorge B. de Macedo, 1978. "Exchange Rates and the International Adjustment Process," Cowles Foundation Discussion Papers 488, Cowles Foundation for Research in Economics, Yale University.
    48. Breidt, F. J. & Carriquiry, Alicia L., 1996. "Improved Quasi-Maximum Likelihood for Stochastic Volatility Models," Staff General Research Papers Archive 1143, Iowa State University, Department of Economics.
    49. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    50. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    51. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    52. Levich, Richard M., 1985. "Empirical studies of exchange rates: Price behavior, rate determination and market efficiency," Handbook of International Economics, in: R. W. Jones & P. B. Kenen (ed.), Handbook of International Economics, edition 1, volume 2, chapter 19, pages 979-1040, Elsevier.
    53. Johansen, Søren & Juselius, Katarina, 1992. "Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 211-244.
    54. Mussa, Michael, 1979. "Empirical regularities in the behavior of exchange rates and theories of the foreign exchange market," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 11(1), pages 9-57, January.
    55. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    56. Juselius, Katarina, 1992. "Domestic and foreign effects on prices in an open economy: The case of Denmark," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 401-428, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    2. Font, Begoña, 1998. "Modelización de series temporales financieras. Una recopilación," DES - Documentos de Trabajo. Estadística y Econometría. DS 3664, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Dibooglu, Selahattin, 1993. "Multiple cointegration and structural models: applications to exchange rate determination," ISU General Staff Papers 1993010108000011419, Iowa State University, Department of Economics.
    4. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, January.
    5. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    6. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    7. Ibrahim Chowdhury & Lucio Sarno, 2004. "Time‐Varying Volatility in the Foreign Exchange Market: New Evidence on its Persistence and on Currency Spillovers," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(5‐6), pages 759-793, June.
    8. John D. Levendis, 2018. "Time Series Econometrics," Springer Texts in Business and Economics, Springer, number 978-3-319-98282-3, June.
    9. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    10. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    11. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    12. Bauer, Rob M M J & Nieuwland, Frederick G M C & Verschoor, Willem F C, 1994. "German Stock Market Dynamics," Empirical Economics, Springer, vol. 19(3), pages 397-418.
    13. Ericsson, Neil R & Hendry, David F & Mizon, Grayham E, 1998. "Exogeneity, Cointegration, and Economic Policy Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 370-387, October.
    14. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    15. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    16. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871.
    17. Tim Bollerslev & Ray Y. Chou & Narayanan Jayaraman & Kenneth F. Kroner - L, 1991. "es modéles ARCH en finance : un point sur la théorie et les résultats empiriques," Annals of Economics and Statistics, GENES, issue 24, pages 1-59.
    18. Committee, Nobel Prize, 2003. "Time-series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity," Nobel Prize in Economics documents 2003-1, Nobel Prize Committee.
    19. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911.
    20. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:isu:genstf:1997010108000012997. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Curtis Balmer (email available below). General contact details of provider: https://edirc.repec.org/data/deiasus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.