Wild bootstrap Ljung-Box test for autocorrelation in vector autoregressive and error correction models

벡터자기회귀모형과 오차수정모형의 자기상관성을 위한 와일드 붓스트랩 Ljung-Box 검정

Lee, Myeongwoo;Lee, Taewook

  • Received : 2015.12.02
  • Accepted : 2015.12.23
  • Published : 2016.02.29


We consider the wild bootstrap Ljung-Box (LB) test for autocorrelation in residuals of fitted multivariate time series models. The asymptotic chi-square distribution under the IID assumption is traditionally used for the LB test; however, size distortion tends to occur in the usage of the LB test, due to the conditional heteroskedasticity of financial time series. In order to overcome such defects, we propose the wild bootstrap LB test for autocorrelation in residuals of fitted vector autoregressive and error correction models. The simulation study and real data analysis are conducted for finite sample performance.


Ljung-Box test;vector autoregressive model;vector error correction model;Wild bootstrap


  1. Ahlgren, N. and Catani, P. (2012). Wild bootstrap tests for autocorrelation in vector autoregressive models, Working Papers 562, Available from:
  2. Bruggemann, R., Lutkepohl, H., and Saikkonen, P. (2006). Residual autocorrelation testing for vector error correction models, Journal of Econometrics, 134, 579-604.
  3. Catani, P., Terasvirta, T., and Yin, M. (2014). A lagrange multiplier test for testing the adequacy of the constant conditional correlation GARCH Model. CREATES Research Paper 2014-3, Available from:
  4. Davidson, R. and Flachaire, E. (2008). The wild bootstrap, Journal of Econometrics, 146, 162-169.
  5. Goncalves, S. and Kilian, L. (2004). Bootstrap autoregressions with conditional heteroskedasticity of unknown form, Journal of Econometrics, 123, 89-120.
  6. Hosking, J. R. M. (1980). The multivariate portmanteau statistic, Journal of the American Statistical Association, 75, 602-608.
  7. Kwon, D. and Lee, T. (2014). Hedging effectiveness of KOSPI200 index futures through VECM-CC-GARCH model, Journal of the Korean Data Information Science Society, 25, 1449-1466.
  8. Li, W. K. and McLeod, A. I. (1981). Distribution of the residual autocorrelation in multivariate ARMA time series models, Journal of the Royal Statistical Society, Series B, 43, 231-239.
  9. Liu, R. (1988). Bootstrap procedures under some non-i.i.d. models, Annals of Statistics, 16, 1696-1708.
  10. Ljung, G. M. and Box, G. E. P. (1978). On a measure of lack of fit in time series models, Biometrika, 65, 297-303.
  11. Mammen, E. (1993). Bootstrap and wild bootstrap for high dimensional linear models, Annals of Statistics, 21, 255-285.
  12. Tsay, R. S. (2010). Analysis of Financial Time Series, 2nd ed, John Wiley & Sons, New Jersey.
  13. Tsay, R. S. (2014). Multivariate Time Series with R and Financial Applications, John Wiley & Sons, New Jersey.


Supported by : 한국외국어대학교