Skip to main content
Log in

On Jackknife-After-Bootstrap Method for Dependent Data

  • Published:
Computational Economics Aims and scope Submit manuscript

Abstract

In this paper, we adapt sufficient and ordered non-overlapping block bootsrap methods into jackknife-after-bootstrap (JaB) algorithm to estimate the standard error of a statistic where observations form a stationary sequence. We also extend the JaB algorithm to obtain prediction intervals for future returns and volatilities of GARCH processes. The finite sample properties of the proposed methods are illustrated by an extensive simulation study and they are applied to S&P 500 stock index data. Our findings reveal that the proposed algorithm often exhibits improved performance and, is computationally more efficient compared to conventional JaB method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Andersen, T. G., & Bollerslev, T. (1998). Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International Economic Review, 39(4), 885–905.

    Article  Google Scholar 

  • Andersen, T. G., Bollerslev, T., Diebold, F. X., & Labys, P. (2001). The distribution of realized exchange rate volatility. Journal of the American statistical Association, 96(453), 42–55.

    Article  Google Scholar 

  • Baillie, R. T., & Bollerslev, T. (1992). Prediction in dynamic models with time-dependent conditional variances. Journal of Econometrics, 52(1), 91–113.

    Article  Google Scholar 

  • Bentes, S. R. (2015). A comparative analysis of the predictive power of implied volatility indices and garch forecasted volatility. Physica A: Statistical Mechanics and its Applications, 424, 105–112.

    Article  Google Scholar 

  • Beyaztas, B., Firuzan, E., & Beyaztas, U. (2016). New block bootstrap methods: Sufficient and/or ordered. Communications in Statistics-Simulation and Computation, 46(5), 3942–3951.

    Google Scholar 

  • Beyaztas, U., & Alin, A. (2013). Jackknife-after-bootstrap method for detection of influential observations in linear regression models. Communications in Statistics-Simulation and Computation, 42(6), 1256–1267.

    Article  Google Scholar 

  • Beyaztas, U., & Alin, A. (2014a). Sufficient jackknife-after-bootstrap method for detection of influential observations in linear regression models. Statistical Papers, 55(4), 1001–1018.

    Article  Google Scholar 

  • Beyaztas, U., & Alin, A. (2014b). Jackknife-after-bootstrap as logistic regression diagnostic tool. Communications in Statistics-Simulation and Computation, 43(9), 2047–2060.

    Article  Google Scholar 

  • Beyaztas, U., & Alin, A. (2014c). Delete-2 jackknife-after-bootstrap in regression. Quality and Reliability Engineering International, 30(7), 993–1002.

    Article  Google Scholar 

  • Beyaztas, U., Alin, A., & Michael, M. A. (2014). Robust bcajab method as a diagnostic tool for linear regression models. Journal of Applied Statistics, 41(7), 1593–1610.

    Article  Google Scholar 

  • Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327.

    Article  Google Scholar 

  • Bougerol, P., & Picard, N. (1992a). Strict stationarity of generalized autoregressive processes. The Annals of Probability, 20(4), 1714–1730.

    Article  Google Scholar 

  • Bougerol, P., & Picard, N. (1992b). Stationarity of garch processes and of some nonnegative time series. Journal of Econometricsy, 52(1), 115–127.

    Article  Google Scholar 

  • Carles, P. G. (2005). Tests of long memory: A bootstrap approach. Computational Economics, 25(1), 103–113.

    Article  Google Scholar 

  • Carlstein, E. (1986). Tests of long memory: A bootstrap approach. The Annals of Statistics, 14(3), 1171–1179.

    Article  Google Scholar 

  • Chen, B., Gel, Y. R., Balakrishna, N., & Abraham, B. (2011). Computationally efficient bootstrap prediction intervals for returns and volatilities in arch and garch processes. Journal of Forecasting, 30(1), 51–71.

    Article  Google Scholar 

  • Dyhrberg, A. H. (2016). Bitcoin, gold and the dollar a garch volatility analysis. Finance Research Letters, 16, 85–92.

    Article  Google Scholar 

  • Efron, B. (1979). Bootstrap methods: another look at the jackknife. The Annals of Statistics, 7(1), 1–26.

    Article  Google Scholar 

  • Efron, B. (1992). Jackknife-after-bootstrap standard errors and influence functions. Journal of the Royal Statistical Society, Series B, 54(1), 83–127.

    Google Scholar 

  • Engle, R. F., & Patton, A. J. (2001). What good is a volatility model. Quantitative Finance, 1(2), 237–245.

    Article  Google Scholar 

  • Gneiting, T., & Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association, 102(477), 359–377.

    Article  Google Scholar 

  • Hall, P., Horowitz, J. L., & Jing, B. (1995). On blocking rules for the bootstrap with dependent data. Biometrika, 82(3), 561–574.

    Article  Google Scholar 

  • Hannan, E. J., & Rissanen, J. (1982). Recursive estimation of mixed autoregressive-moving average order. Biometrika, 69(1), 81–94.

    Article  Google Scholar 

  • Kunsch, H. R. (1989). The jackknife and the bootstrap for general stationary observations. The Annals of Statistics, 17(3), 1217–1241.

    Article  Google Scholar 

  • Lahiri, S. N. (2002). On the jackknife-after-bootstrap method for dependent data and its consistency properties. Econometric Theory, 18(1), 79–98.

    Article  Google Scholar 

  • Lama, A., Jha, G. K., Paul, R. K., & Gurung, B. (2015). Modelling and forecasting of price volatility: An application of garch and egarch models. Agricultural Economics Research Review, 28, 365–382.

    Article  Google Scholar 

  • Limma, E. J. A., & Tabak, B. M. (2009). Tests of random walk: A comparison of bootstrap approaches. Computational Economics, 34, 365–382.

    Article  Google Scholar 

  • Liu, RY., Singh, K. (1992). Moving blocks jackknife and bootstrap capture weak dependence. Exploring the Limits of Bootstrap (pp. 225–248).

  • Michael, M. A., & Roberts, S. (2010). Jackknife-after-bootstrap regression influence diagnostics. Journal of Nonparametric Statistics, 22(2), 257–269.

    Article  Google Scholar 

  • Miguel, J. A., & Olave, P. (1999). Bootstrapping forecast intervals in arch models. Test, 8(2), 345–364.

    Article  Google Scholar 

  • Pascual, L., Romo, J., & Ruiz, E. (2006). Bootstrap prediction for returns and volatilities in garch models. Computational Statistics & Data Analysis, 50(9), 2293–2312.

    Article  Google Scholar 

  • Reeves, J. J. (2005). Bootstrap prediction intervals for arch models. International Journal of Forecasting, 21(2), 237–248.

    Article  Google Scholar 

  • Singh, S., & Sedory, S. A. (2011). Sufficient bootstrapping. Computational Statistics & Data Analysis, 55(4), 1629–1637.

    Article  Google Scholar 

  • Sotiriadis, M. S., Tsotsos, R., & KosmidouEmail, K. (2016). Price and volatility interrelationships in the wholesale spot electricity markets of the Central-Western European and nordic region: A multivariate garch approach. Energy Systems, 7(1), 5–32.

    Article  Google Scholar 

Download references

Acknowledgements

We thank two anonymous referees for careful reading of the paper and valuable suggestions and comments, which have helped us produce a significantly better paper. We are also grateful to the Editor for offering the opportunity to publish our work.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ufuk Beyaztas.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Beyaztas, U., Beyaztas, B.H. On Jackknife-After-Bootstrap Method for Dependent Data. Comput Econ 53, 1613–1632 (2019). https://doi.org/10.1007/s10614-018-9827-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10614-018-9827-4

Keywords

Mathematics Subject Classification

Navigation