Abstract
We review different methods of bootstrapping or subsampling financial time series.We first discuss methods that can be applied to generate pseudo-series of log-returns which mimic closely the essential dependence characteristics of the observed series. We then review methods that apply the bootstrap in order to infer properties of statistics based on financial times series. Such methods do not work by generating new pseudo-series of the observed log-returns but by generating pseudo-replicates of the statistic of interest. Finally, we discuss subsampling and self-normalization methods applied to financial data.
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
Ango Nze, P., Bühlmann, P. and Doukhan, P. (2002): Weak dependence beyond mixing and asymptotics for nonparametric regression. Annals of Statistics 30, 397–430.
Ango Nze, P., Dupoiron, S. and Rios, R. (2003): Subsampling under weak dependence conditions. Tech. Report DT2003–42. CREST, Paris.
Berkes, I., Horváth, L. and Kokoszka, P. (2003): GARCH processes: structure and estimation. Bernoulli 9, 201–228.
Bertail, P., Politis, D. N. and Romano, J. P. (1999): On subsampling estimators with unknown rate of convergence. Journal of the American Statistical Association 94, 569–579.
Bollerslev, T. (1986): Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics 31, 307–327.
Bougerol, P. and Picard, N. (1992): Stationarity of GARCH processes and of some non-negative time series. Journal of Econometrics 52, 115–127.
Bühlmann, P. (2002): Bootstrap for time series. Statistical Science 17, 52–72.
Carlstein, E. (1986): The use of subseries values for estimating the variance of a general statistic from a stationary time series. Annals of Statistics 14, 1171–1179.
Carrasco, M. and Chen, X. (2002): Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 18, 17–39.
Doukhan, P. and Louhichi, S. (1999): A new weak dependence condition and applications to moment inequalities. Stochastic Processes and its Applications 84, 313–342.
Engle, R. (1982): Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica 50, 987–1008.
Fan, J. and Yao, Q. (1998): Efficient estimation of conditional variance functions in stochastic regression. Biometrika 85, 645–660.
Franke, J., Kreiss, J.-P. and Mammen, E. (2002a): Bootstrap of kernel smoothing in nonlinear time series. Bernoulli 8, 1–37.
Franke, J., Kreiss, J.-P., Mammen, E. and Neumann, M. H. (2002b): Properties of the nonparametric autoregressive bootstrap. Journal of Time Series Analysis 23, 555–585.
Franke, J., Neumann, M. H. and Stockis, J. P. (2004): Bootstrapping nonparametric estimators of the volatility function. Journal of Econometrics 118, 189–218.
Giraitis, L., Kokoszka, P. and Leipus, R. (2000): Stationary ARCH models: Dependence structure and central limit theorem. Econometric Theory 16, 3–22.
Hall, P. (1992): The bootstrap and Edgeworth expansion. Springer Verlag, New York.
Hall, P., Jing, B.-Y. and Lahiri, S. N. (1998): On the sampling window method for long-range dependent data. Statistica Sinica 8, 1189–1204.
Hall, P. and Yao, Q. (2003): Inference in ARCH and GARCH models with heavy-tailed errors. Econometrica 71, 285–317.
Härdle, W., Horowitz, J. and Kreiss, J.-P. (2003): Bootstrap for Time Series. International Statistical Review 71, 435–459.
Hart, J. D. (1995): Some automated methods of smoothing time-dependent data. Journal of Nonparametric Statistics 6, 115–142.
Horowitz, J.L. (2003): Bootstrap methods for Markov processes. Econometrica 71, 1049–1082.
KazakevičDius, V. and Leipus, R. (2002): On stationarity in the ARCH(∞) model. Econometric Theory 18, 1–16.
Kokoszka, P., Teyssiére, G. and Zhang, A.(2004): Confidence intervals for the autocorrelations of the squares of GARCH sequences. In: Bubak, M. et al. (Eds.): ICCS, 827–834. Springer, Berlin.
Kokoszka, P. and Wolf, M. (2004): Subsampling the mean of heavy-tailed dependent observations. Journal of Time Series Analysis 25, 217–234.
Kreiss, J.-P. (2000): Nonparametric estimation and bootstrap for financial time series. In: Chan, W. S., Li, W. K. and Tong, H. (Eds.): Statistics and Finance: An Interface. London, Imperial College Press.
Kreiss, J.-P., Neumann, M. H. and Yao, Q. (2008): Bootstrap tests for simple structures in nonparametric time series regression. Statistics and Its Interface to appear.
Künsch, H. R. (1989): The jackknife and the bootstrap for general stationary observations. Annals of Statistics 17, 1217–1241.
Lahiri, S. N. (2003): Resampling methods for dependent data. Springer, New York.
Liu, R. and Singh, K. (1992): Moving blocks jackknife and bootstrap capture weak dependence. In: LePage, R. and Billard, L. (Eds.): Exploring the limits of the bootstrap, 225–248. Wiley, New York.
Maddala, G. S. and Li, H. (1996): Bootstrap based tests in financial models. In: Maddala, G. S. and Rao, C. R. (Eds.): Handbook of Statistics 14, 463–488. Amsterdam, Elsevier.
Mammen, E. (1992): When does the bootstrap work? Asymptotic results and simulations. Springer Lecture Notes in Statistics 77. Singer Verlag, Heidelberg.
McElroy, T. and Politis, D. N. (2002): Robust inference for the mean in the presence of serial correlation and heavy tailed distributions. Econometric Theory 18, 1019–1039.
McElroy, T. and Politis, D. N. (2006): Self-Normalization for heavy-tailed time series with long memory. Statistica Sinica to appear.
Miquel, J. A. and Olave, P. (1999): Bootstrapping forecast intervals in ARCH models. Test 8, 345–364.
Neumann, M. H. and Kreiss, J.-P. (1998): Regression type inference in nonparametric autoregression. Annals of Statistics 26, 1570–1613.
Paparoditis, E. and Politis, D. N. (2000): The local bootstrap for kernel estimators under general dependence conditions. Annals of the Institute of Statistical Mathematics 52, 139–159.
Paparoditis, E. and Politis, D. N. (2001a): The local bootstrap for Markov processes. Journal of Statistical Planning and Inference 108, 301–328.
Paparoditis, E. and Politis, D. N. (2002): A Markovian local resampling scheme for nonparametric estimators in time series analysis. Econometric Theorey 17, 540–566.
Paparoditis, E. and Politis, D. N. (2003): Residual-based block bootstrap for unit root testing. Econometrica 71, 813–855.
Politis, D. N. (2003): The impact of bootstrap methods on time series analysis. Statistical Science 18, 219–230.
Politis, D. N. and Romano, J. P. (1994): Large sample confidence regions based on sub-samples under minimal assumptions. Annals of Statistics 22, 2031–2050.
Politis, D. N. and Romano, J. P. (1994): The stationary bootstrap. Journal of the American Statistical Association 89, 1303–1313.
Politis, D. N., Romano, J. P. and Wolf, M. (1997): Subsampling for heteroskestastic time series. Journal of Econometrics 81, 281–317.
Politis, D. N., Romano, J. P. and Wolf, M. (1999): Subsampling. Springer Verlag, New York.
Politis, D. N., Romano, J. P. and Wolf, M. (2004): Inference for Autocorrelations in the Possible Presence of a Unit Root. Journal of Time Series Analysis 25, 251–263.
Rajarshi, M. B. (1990): Bootstrap in Markov-sequences based on estimates of transition densities. Annals of the Institute of Statistical Mathematics 42, 253–268.
Robinson, P. (1983): Nonparametric estimators for time series. Journal of Time Series Analysis 4, 185–207.
Robinson, P. (2001): Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression. Journal of Econometrics 47, 67–84.
Romano, J. P. and Wolf, M. (2001): Subsampling intervals in autoregressive models with linear time trend. Econometrica 69, 1283–1314.
Ruiz, E. and Pascual, L. (2002): Bootstrapping financial time series. Journal of Economic Surveys 16, 271–300.
Shepard, N. (1996): Statistical aspects of ARCH and stochastic volatility. In: Cox, D. R. and Hinkley, D. V. (Eds.): Time series models in Econometrics, Finance and other fields, 1–67. Capman and Hall, London.
Shi, S. G. (1991): Local bootstrap. Annals of the Institute of Statistical Mathematics. 43, 667–676.
Straumann, D. (2005): Estimation in conditionally heteroscedastic time series models. Lecture Notes in Statistics 181. Springer Verlag, Berlin.
Taylor, S. (1986): Modelling financial time series. Wiley, New York.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Paparoditis, E., Politis, D.N. (2009). Resampling and Subsampling for Financial Time Series. In: Mikosch, T., Kreiß, JP., Davis, R., Andersen, T. (eds) Handbook of Financial Time Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71297-8_42
Download citation
DOI: https://doi.org/10.1007/978-3-540-71297-8_42
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71296-1
Online ISBN: 978-3-540-71297-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)