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2019 | OriginalPaper | Chapter

15. Non-Parametric and Flexible Time Series Estimators

Authors : Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner

Published in: Statistics of Financial Markets

Publisher: Springer International Publishing

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Abstract

With the analysis of (financial) time series, one of the most important goals is to produce forecasts. Using past data one can argue about the future mean, the future volatility and so on; however, a flexible method of producing such estimates will be introduced in this chapter.

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Literature
Ango Nze, P. (1992). Critères d’ergodicité de quelques modèles à représentation markovienne. Technical Report 315, ser. 1. Paris: C.R. Acad. Sci.
Bossaerts, P., & Hillion, P. (1993). Test of a general equilibrium stock option pricing model. Mathematical Finance, 3, 311–347.CrossRef
Carroll, R. J., Härdle, W., & Mammen, E. (2002). Estimation in an additive model when the components are linked parametrically. Econometric Theory, 18, 886–912.MathSciNetCrossRef
Chan, K., & Tong, H. (1985). On the use of deterministic Lyapunov functions for the ergodicity of stochastic difference equations. Advanced Applied Probability, 17, 666–678.MathSciNetCrossRef
Chen, R., & Tsay, R. S. (1993a). Functional-coefficient autoregressive models. Journal of the American Statistical Association, 88, 298–308.MathSciNetMATH
Chen, R., & Tsay, R. S. (1993b). Nonlinear additive ARX models. Journal of the American Statistical Association, 88, 955–967.CrossRef
Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74, 829–836.MathSciNetCrossRef
Collomb, G. (1984). Propriétés de convergence presque complète du prédicteur à noyau. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 66, 441–460.MathSciNetCrossRef
Diebolt, J., & Guégan, D. (1990). Probabilistic properties of the general nonlinear autoregressive process of order one. Technical Report 128. Paris: Université de Paris VI.
Doukhan, P., & Ghindès, M. (1980). Estimation dans le processus xn+1 = f(xn) + εn+1. C.R. Acad. Sci. Paris, Sér. A, 297, 61–64.MATH
Doukhan, P., & Ghindès, M. (1981). Processus autorégressifs non-linéaires. C.R. Acad. Sci. Paris, Sér. A, 290, 921–923.MATH
Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987–1008.MathSciNetCrossRef
Engle, R. F., & Gonzalez-Rivera, G. (1991). Semiparametric ARCH models. Journal of Business and Economic Statistics, 9, 345–360.
Fan, J., & Gijbels, I. (1996). Local polynomial modeling and its application – Theory and methodologies. Chapman and Hall.MATH
Fan, J., & Yao, Q. (1998). Efficient estimation of conditional variance functions in stochastic regression. Biometrika, 85, 645–660.MathSciNetCrossRef
Fan, J., & Yao, Q. (2003). Nonlinear time series: Nonparametric and parametric methods. New York: Springer-Verlag.CrossRef
Föllmer, H., & Schweizer, M. (1991). Hedging of contingent claims under incomplete information. In M. H. A. Davis, & R. J. Elliot (Eds.), Applied stochastic analysis (pp. 389–414). London: Gordon and Breach.
Föllmer, H., & Sondermann, D. (1991). Hedging of non-redundant contingent claims. In W. Hildenbrand, & A. Mas-Colell (Eds.), Contributions to mathematical economics (pp. 205–223). North Holland: Amsterdam.
Franke, J. (1999). Nonlinear and nonparametric methods for analyzing financial time series. In P. Kall, & H.-J. Luethi (Eds.), Operation research proceedings 98, Heidelberg: Springer-Verlag.
Franke, J., Härdle, W., & Kreiss, J. (2003). Nonparametric estimation in a stochastic volatility model. Recent Advances and Trends in Nonparametric Statistics, 303–314.
Franke, J., Kreiss, J., & Mammen, E. (2002). Bootstrap of kernel smoothing in nonlinear time series. Bernoulli, 8(1), 1–37.MathSciNetMATH
Glosten, L., Jagannathan, R., & Runkle, D. (1993). On the relationship between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48, 1779–1801.CrossRef
Gregory, A. (1989). A nonparametric test for autoregressive conditional heteroscedasticity: A Markov chain approach. Journal of Business and Economic Statistics, 7, 107–115.
Hafner, C. (1998). Estimating high frequency foreign exchange rate volatility with nonparametric ARCH models. Journal of Statistical Planning and Inference, 68, 247–269.MathSciNetCrossRef
Härdle, W. (1990). Applied nonparametric regression. Cambridge: Cambridge University Press.CrossRef
Härdle, W., & Hafner, C. (2000). Discrete time option pricing with flexible volatility estimation. Finance and Stochastics, 4, 189–207.MathSciNetCrossRef
Härdle, W., Lütkepohl, H., & Chen, R. (1997). Nonparametric time series analysis. International Statistical Review, 12, 153–172.MATH
Härdle, W., Müller, M., Sperlich, S., & Werwatz, A. (2004). Non- and semiparametric modelling. Heidelberg: Springer-Verlag.CrossRef
Härdle, W., & Tsybakov, A. (1997). Local polynomial estimation of the volatility function. Journal of Econometrics, 81, 223–242.MathSciNetCrossRef
Härdle, W., Tsybakov, A., & Yang, L. (1996). Nonparametric vector autoregression. Journal of Statistical Planning and Inference, 68, 221–245.MathSciNetCrossRef
Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42, 281–300.CrossRef
Katkovnik, V. (1979). Linear and nonlinear methods for nonparametric regression analysis (in Russian). Avtomatika i Telemehanika, 35–46.
Katkovnik, V. (1985). Nonparametric identification and data smoothing. Nauka.MATH
McKeague, I., & Zhang, M. (1994). Identification of nonlinear time series from first order cumulative characteristics. Annals of Statistics, 22, 495–514.MathSciNetCrossRef
Melino, A., & Turnbull, S. M. (1990). Pricing foreign currency options with stochastic volatility. Journal of Econometrics, 45, 239–265.CrossRef
Mokkadem, A. (1987). Sur un modèle autorégressif nonlinéaire. ergodicité et ergodicité géometrique. Journal of Time Series Analysis, 8, 195–204.MathSciNetCrossRef
Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59, 347–370.MathSciNetCrossRef
Rabemananjara, R., & Zakoian, J. M. (1993). Threshold ARCH models and asymmetries in volatility. Journal of Applied Econometrics, 8, 31–49.CrossRef
Renault, E., & Touzi, N. (1996). Option hedging and implied volatilities in a stochastic volatility model. Mathematical Finance, 6, 277–302.CrossRef
Robinson, P. (1983). Non-parametric estimation for time series models. Journal of Time Series Analysis, 4, 185–208.MathSciNetCrossRef
Robinson, P. (1984). Robust nonparametric autoregression. In J. Franke, W. Härdle, & Martin (Eds.), Robust and nonlinear time series analysis. Heidelberg: Springer-Verlag.
Tong, H. (1983). Threshold models in nonlinear time series analysis, Vol. 21 of Lecture notes in statistics. Heidelberg: Springer-Verlag.CrossRef
Tsybakov, A. (1986). Robust reconstruction of functions by the local-approximation method. Problems of Information Transmission, 22, 133–146.MathSciNetMATH
Vieu, P. (1995). Order choice in nonlinear autoregressive models, Discussion Paper, Laboratoire de Statistique et Probabilités, Université Toulouse.MATH
Wiggins, J. (1987). Option values under stochastic volatility: Theory and empirical estimates. Journal of Financial Economics, 19.CrossRef
Yang, L., Härdle, W., & Nielsen, J. (1999). Nonparametric autoregression with multiplicative volatility and additive mean. Journal of Time Series Analysis, 20(5), 579–604.MathSciNetCrossRef
Zakoian, J. (1994). Threshold heteroskedastic functions. Journal of Economic Dynamics and Control, 18, 931–955.CrossRef
Metadata
Title
Non-Parametric and Flexible Time Series Estimators
Authors
Jürgen Franke
Wolfgang Karl Härdle
Christian Matthias Hafner
Copyright Year
2019
Book
Statistics of Financial Markets

Print ISBN: 978-3-030-13750-2

Electronic ISBN: 978-3-030-13751-9

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-13751-9_15