Résumés
Abstract
In this paper, we propose a novel entropy-based resampling scheme valid for non-stationary data. In particular, we identify the reason for the failure of the original entropy-based algorithm of Vinod and López-de Lacalle (2009) to be the perfect rank correlation between the actual and bootstrapped time series. We propose the Maximum Entropy Block Bootstrap which preserves the rank correlation locally. Further, we also introduce the Maximum non-extensive Entropy Block Bootstrap to allow for fat tail behaviour in time series. Finally, we show the optimal finite sample properties of the proposed methods via a Monte Carlo analysis where we bootstrap the distribution of the Dickey-Fuller test.
Parties annexes
Bibliography
- Buhlmann, P. (1997). “Sieve Bootstrap for Time Series.’’ Bernoulli, 3: 123–148.10.2307/3318584 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Davidson, R. and A. Monticini (2014). “Heteroskedasticity-and-autocorrelation- consistent Bootstrapping.’’ Technical report, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).10.1214/aos/1176344552 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Efron, B. (1979). “Bootstrap Methods: Another Look at the Jackknife.’’ Annals of Statistics, 7: 1–26.10.1214/aos/1176344552 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Künsch, H. (1989). “The Jack-knife and the Bootstrap for General Stationary Observations.’’ Annals of Statistics, 17: 1217–1241.10.1214/aos/1176347265 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Mammen, E. (1993). “Bootstrap and Wild Bootstrap for High Dimensional Linear Models.’’ Annals of Statistics, 21: 255–285.10.1214/aos/1176349025 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Palm, F. C., S. Smeekes, and J.-P. Urbain (2007). “Bootstrap Unit-Root Tests: Comparisons and Extensions.’’ Journal of Time Series Analysis, 29: 371–401.10.1111/j.1467-9892.2007.00565.x Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Paparoditis, E., and D. Politis (2001). “The Continuous Path Block-Bootstrap.’’ In Puri, M. (Ed.), Asymptotics in Statistics and Probability, pp. 305–320. VSP Publications.10.1007/978-1-4612-1554-7 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Phillips, P. C. B. (2010). “Bootstrapping I(1) Data.’’ Journal of Econometrics, 158: 280–284.10.1016/j.jeconom.2010.01.010 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Politis, D., J. Romano, and M. Wolf (1999). Subsampling. Springer Series in Statistics. Springer New York.10.1007/978-1-4612-1554-7 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Tsallis, C. (1988). “Possible Generalization of Boltzmann-Gibbs Statistics.’’ Journal of Statistical Physics, 52: 479–487.10.1007/BF01016429 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Vinod, H. D. and J. López-de Lacalle (2009). “Maximum Entropy Bootstrap for Time Series: The Meboot R Package.’’ Journal of Statistical Software, 29: 1–19.10.18637/jss.v029.i05 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Wu, C.-F. J. (1986). “Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis.’’ Annals of Statistics, 14: 1261–1295.10.1214/aos/1176350142 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
