Forecasting properties of a new method to determine optimal lag order in stable and unstable VAR models

Abstract

This simulation study investigates the forecasting performance of a new information criterion suggested by Hatemi-J (2003) to pick the optimal lag length in the stable and unstable vector autregression (VAR) models. The conducted Monte Carlo experiments reveal that this information criterion is successful in selecting the optimal lag order in the VAR model when the main aim is to draw ex-ante (forecasting) inference regardless if the VAR model is stable or not. In addition, the simulations indicate that this information criterion is robust to autoregressive conditional heteroskedasticity effects.

Notes

¹ The first information criterion for choosing the optimal lag order was introduced by Akaike (1969). Two other most commonly used criteria are SBC, suggested by Schwarz (1978), and HQC, suggested by Hannan and Quinn (1979). According to the literature, SBC as well as HQC is consistent, which means the probability of selecting the true lag order in a VAR model converges to one asymptotically. According to Nielsen (2001), the consistency property of these two criteria holds irrespective of the properties of the characteristic roots in the VAR model. HJC shares the consistency property of SBC and HQC because it is a linear function of the two.

² It should be mentioned that HJC can also be used for determining the lag order in a univariate (single equation) model. The univariate form of HJC is the following:

where σ² is the variance of the residuals and k is the number of parameters that are estimated in the regression.

³ It should be mentioned that this is the same parameter set as it was used by Hatemi-J (2003).

⁴ The ARCH model was originally introduced by Engle (1982).

⁵ The formal derivation of Equation 11 is based on Hatemi-J (2004) article.

⁶ For comparability and parsimonious use of the random number generator from a N(0, 1) distribution, the random number drawn is initially the same for homoskedastic and ARCH versions with the ARCH version subsequently multiplying draws by an appropriate time varying number to modify the variable.

⁷ Note that our forecasting horizon is five, i.e. h = 1, 2, … , 5.

⁸ See also Lütkepohl (1991).

⁹ A program procedure written in GAUSS for applying HJC in applied research is available from the author upon request.