Size Refinement of Empirical Likelihood Tests in Time Series Models using Sieve Bootstraps

Lee, Jin

  • Received : 2013.03.22
  • Accepted : 2013.05.21
  • Published : 2013.05.31


We employ sieve bootstraps for empirical likelihood tests in time series models because their null distributions are often vulnerable to the presence of serial dependence. We found a significant size refinement of the bootstrapped versions of a Lagrangian Multiplier type test statistic regardless of the bandwidth choice required by long-run variance estimations.


Time series;empirical likelihood;size of the test;sieve bootstrap


  1. Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation, Econometrica, 59, 817-858.
  2. Buhlman, P. (1997). Sieve bootstrap for time series, Bernoulli, 3, 123-148.
  3. Chang, Y. and Park, J. (2004). A sieve bootstrap for the test of a unit root, Journal of Time Series Analysis, 24, 379-400.
  4. Guggenberger, P. and Smith, R. (2008). Generalized empirical likelihood tests in time series models with potential identification failure, Journal of Econometrics, 142, 134-161.
  5. Kitamura, Y. (1997). Empirical likelihood methods with weakly dependent processes, Annals of Statistics, 25, 2084-2102.
  6. Kitamura, Y. and Stutzer, M. (1997). An information-theoretic alternative to generalized method of moments estimations, Econometrica, 65, 861-874.
  7. Kleibergen, F. (2005). Testing parameters in GMM without assuming that they are identified, Econometrica, 73, 1103-1123.
  8. Newey, W. and Smith, R. (2004). Higher order properties of GMM and empirical likelihood estimators, Econometrica, 72, 219-255.
  9. Newey, W. and West, K. (1994). Automatic lag selection in covariance matrix estimation, Review of Economic Studies, 61, 631-653.
  10. Otsu, T. (2006). Generalized empirical likelihood inference for nonlinear and time series models under weak identification, Econometric Theory, 22, 513-527.
  11. Palm, F. C., Smeekes, S. and Urbain, J.-P. (2010). A sieve bootstrap test for cointegration in a conditional error correction model, Econometric Theory, 26, 647-681.
  12. Park, J. (2002). An Invariance Principle for sieve bootstrap in time series, Econometric Theory, 18, 469-490.
  13. Stock, J. and Wright, J. (2000). GMM with weak identification, Econometrica, 68, 1055-1096.


Supported by : National Research Foundation of Korean