Abstract
The statistical properties of three foreign exchange rate series are analyzed using a redefinition of the time scale to cope with the inherent seasonal heteroskedasticity. A conditional heteroskedastic autoregressive nonlinear (CHARN) model is estimated by local linear regression techniques. The results show significant nonlinearities for the mean function as well as for the variance function.
Comments on a preliminary presentation at the fifth (EC)2 conference are gratefully acknowledged. The XploRe macros for local polynomial estimation and the data were generously provided by Marlene Müller and Olsen Associates, respectively.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baillie, R. T. and Bollerslev, T. (1990) Intra-day and inter-market volatility in foreign exchange rates, Review of Economic Studies 58: 565–585.
Bossaerts, P., Härdle, W. and Hafner, C. (1995) Foreign exchange rates have surprising volatility, Discussion Paper, Humboldt-Universität zu Berlin.
Chen, R. and Tsay, R. S. (1993) Nonlinear additive arx models, Journal of the American Statistical Association 88: 955–967.
Drost, F. C. and Nijman, T. E. (1993) Temporal Aggregation of GARCH processes, Econometrica 61: 909–927.
Engle, R. F. and González-Rivera, G. (1991) Semiparametric ARCH models, Journal of Business & Economic Statistics 9: 345–359.
Fan, J. and Gijbels, I. (1995) Local polynomial modeling and its application — Theory and methodologies, Chapman and Hall.
Fan, J. and Müller, M. (1995) Density and regression smootheing, in: Härdle, W., Klinke, S. and Turlach, B., XploRe — an interactive statistical computing environment, Springer.
Ghysels, E., Gouriéroux, C. and Jasiak, J. (1994) Market time and asset price movements, theory and estimation, Discussion paper Université de Montréal.
Goodhart, C.A. and Figliuoli, L. (1991) Every minute counts in financial markets, Journal of International Money and Finance 10: 23–52.
Gouriéroux, C. (1992) Modèles ARCH et Applications Financières, Economica.
Gouriéroux, C. and Monfort, A. (1992) Qualitative threshold ARCH models, Journal of Econometrics 52: 159–199.
Guillaume, D.M., Dacorogna, M.M., Davé, R.R., Müller, U.A., Olsen, R.B. and Pictet, O.V. (1994) From the bird’s eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange market, Olsen Associates working paper.
Hardie, W. (1990) Applied nonparametric regression, Cambridge University Press.
Hardie, W. and Tsybakov, A. (1995) Local polynomial estimation of the volatility function, SFB 373 Discussion paper.
Kneip, A. and Engel, J. (1994) A remedy for Kernel regression under random design, Discussion paper SFB 303, Universität Bonn.
Mandelbrot, B. B. and Taylor, H. M. (1967) On the distribution of stock price differences, Operations Research 15: 1057–1062.
Robinson, P. M. (1983) Nonparametric estimators for time series, Journal of Time Series Analysis 4: 185–207.
Stock, J. H. (1988) Estimating continuous time processes subject to time deformation, Journal of the American Statistical Association 83 (401): 77–84.
Tsybakov, A. (1986) Robust reconstruction of functions by the local-approximation method, Problems of Information Transmission 22, 133–146.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Physica-Verlag Heidelberg
About this chapter
Cite this chapter
Bossaerts, P., Hafner, C., Härdle, W. (1996). A New Method for Volatility Estimation with Applications in Foreign Exchange Rate Series. In: Bol, G., Nakhaeizadeh, G., Vollmer, KH. (eds) Finanzmarktanalyse und -prognose mit innovativen quantitativen Verfahren. Wirtschaftswissenschaftliche Beiträge, vol 125. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-61489-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-61489-7_4
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-0925-1
Online ISBN: 978-3-642-61489-7
eBook Packages: Springer Book Archive