Selection in VAR-models using equal and unequal lag-length procedures (Q1966361)

Consider the vector time series \(y_t=(y_{1t},\dots,y_{kt})\) generated by a vector autoregressive model which may posses unequal lag-length, i.e. \[ y_{it}= v_i+a_{i1,1}y_{1,t-1}+\dots +a_{i1,p_1}y_{1,t-p_1} + \dots + a_{ik,1}y_{k,t-1}+\dots +a_{ik,p_1}y_{k,t-p_k}, \] \(i=1,\dots,k\). The task is the selection of the \(k\) lag-length \(p_1,\dots,p_k\). If the largest lag-length is \(p\), then there are \((p+1)^{k^2}\) combinations for a whole model. The 2-step Hsiao procedure together with an information criterion allows to reduce the number of investigated combinations, but does not guarantee that the correct specification is found. In this paper the Monte Carlo simulation is applied to analyze and compare the properties of the different lag-length selection strategies based on following information criteria: (1) AIC criteria, (2) Schwarz BIC criterion, (3) Hannan and Quinn's criterion HQ. Seven vector AR models with properties similar to typical macroeconomic time series are used. The true lag-length varies from 1 to 4, with both equal and unequal lag structure. The authors find that the procedures' behaviour seems to be highly model dependent, thus it is difficult to give clear guidelines for choice. The procedures based on equal lag-length together with AIC and HQ well estimate the correct lag-length for models with simple lag structure. For models with more complicated structure where there are holes in the lag polynomials, the unequal Hsiao lag-length procedure may be the better choice.