Lag length estimation in large dimensional systems

Abstract

Abstract. We study the impact of the system dimension on commonly used model selection criteria (AIC, BIC, HQ) and LR based general to specific testing strategies for lag length estimation in VARs. We show that AIC's well known overparameterization feature becomes quickly irrelevant as we move away from univariate models, with the criterion leading to consistent estimates under sufficiently large system dimensions. Unless the sample size is unrealistically small, all model selection criteria will tend to point towards low orders as the system dimension increases, with the AIC remaining by far the best performing criterion. This latter point is also illustrated via the use of an analytical power function for model selection criteria. The comparison between the model selection and general to specific testing strategy is discussed within the context of a new penalty term leading to the same choice of lag length under both approaches.

Counter-urbanisation, planning and house prices: an analysis of the Aberdeen Housing Market Area, 1984-2010

“…The optimal lag length can be determined by alternative criterion (Cheung and Lai, 1993;Gonzalo and Pitarakis, 2002). In this case the optimal lag length of five was selected as determined by the Akaike information criterion (AIC) and the final prediction error (FPE) criterion.…”

A Multivariate Approach for Identification of Optimal Locations with in Ethiopia’s Wheat Market to Tackle Soaring Inflation on Food Price

“…Moreover given lower Chao and Phillips (1999) and others for conflicting result. But more robust analysis is found in study by Gonzalo and Pitarakis (2000) with diverse data generating process. 8 For simulation result about the impact of maximum lag allowed you can see Gonzalo and Pitarakis (2000).…”

“…8 For simulation result about the impact of maximum lag allowed you can see Gonzalo and Pitarakis (2000). 9 Study by Gonzalo and Pitarakis (2000) did show that when longer lags are allowed in small or moderate sample sizes information criterions have tendency to pick the maximum lag allowed. And this is widely observed in this paper.…”

“…This is so since the criterions never select the same lag for any of the dimensions given above. A robust study on lag selection by Gonzalo and Pitarakis (2000) did show that HQIC and SBIC have high probability to under fit and AIC have higher tendency to over fit in small and moderate samples. So the testes are not taken as perfect predictors of the lag order but as minimum and maximum lag identifiers.…”

Testing Twin Deficits Hypothesis using VARs and Variance Decomposition

“…Despite different lag structures in each country, the residuals do not exhibit any form of serial correlation or ARCH effects satisfying the normal specification criteria for the residuals. In addition, the multivariate generalization of AIC remains the best performing criterion as the system dimension increases (see Gonzalo and Pitarakis, 2002).…”