Can the LR test be helpful in choosing the optimal lag order in the VAR model when information criteria suggest different lag orders?

Abstract

The objective of this simulation study is to investigate whether the likelihood ratio (LR) test can pick the optimal lag order in the vector autoregressive model when the most applied information criteria (i.e. vector Schwarz–Bayesian, SBC and vector Hannan–Quinn, HQC) suggest two different lag orders. This lag-choosing procedure has been suggested by Hatemi-J (1999). The results based on the Monte Carlo simulations show that combining the LR test with SBC and HQC causes a substantial increase in the success rate of choosing the optimal lag order compared to cases when only SBC or HQC are used. This appears to be the case irrespective of homoscedasticity or conditional heteroscedasticity properties of the error-term in small sample sizes. This improvement in choosing the right lag order also tends to improve the forecasting capability of the underlying model.

Acknowledgement

We would like to thank the editor of this journal and an anonymous referee for useful comments and suggestions that resulted in an improvement of this article. However, the usual disclaimer applies.

Notes

¹For applications of this approach see Hacker and Hatemi-J (2003a, b) and Gunduz and Hatemi-J (2005).

² For other new approaches to select the optimal lag order see Hatemi-J (2003, 2006) and Bahmani-Oskooee and Brooks (2003).

³ Nielsen (2001) shows that SBC and HQC are consistent regardless of the assumption about the characteristic roots in the VAR model. By consistency is meant that the criterion selects the true order of the VAR system with probability one asymptotically.

⁴ In this formulation of multivariate ARCH the conditional and unconditional variances are equal to each other asymptotically. This seems to be a necessary condition in order to make sure that the comparison of our simulation results for homoscedastic and conditionally heteroscedastic cases makes sense. A mathematical derivation of Equation 5 is provided by Hatemi-J (2004). For a test of multivariate ARCH effects in the VAR model the interested reader is referred to Hacker and Hatemi-J (2005).

⁵ Notice that SBC and HQC choose different lag orders more frequently in small sample sizes. In large sample sizes (asymptotically) both information criteria are expected to choose the same lag order and there will be no need for using the LR test in such cases. That is why we concentrate on small sample sizes in our simulations. However, we also conducted simulations for a sample size of 70. The results, not presented to save space, showed similar qualitative results.

 ⁶ Lütkepohl (1985, 1991) handles his presentation of forecast capability in a different fashion. He focuses not on the systematic forecast error, , but on the overall forecast error , where z_i,T+h is an actualized outcome of z_i for h periods into the future. He thus also includes in his focus the unsystematic (random) components of the forecast error, E(z_i,T+h ) − z_i,T+h , which injects additional randomness that we find undesirable for comparison since it is unsystematic. For his presentation in his 1985 article he normalizes (divides) an approximation of the mean squared overall forecast error with the theoretical variance of E(z_i,T+h ) − z_i,T+h .