Selection of Optimal Lag Length in Cointegrated VAR Models with Weak Form of Common Cyclical Features

Carrasco Gutierrez, Carlos Enrique and Castro Souza, Reinaldo and Teixeira de Carvalho Guillén, Osmani (2009): Selection of Optimal Lag Length in Cointegrated VAR Models with Weak Form of Common Cyclical Features. Published in: Brazilian Review of Econometrics , Vol. 29, No. 1 (2009): pp. 59-78.

Abstract

An important aspect of empirical research based on the vector autoregressive (VAR) model is the choice of the lag order, since all inferences in this model depend on the correct model specification. There have been many studies of how to select the lag order of a nonstationary VAR model subject to cointegration restrictions. In this work, we consider in the model an additional weak form (WF) restriction of common cyclical features to analyze the appropriate way to select the correct lag order. We use two methodologies: the traditional information criteria (AIC, HQ and SC) and an alternative criterion (IC(p;s)) that selects the lag order p and the rank structure, s, due to the WF restriction. We use a Monte-Carlo simulation in the analysis. The results indicate that the cost of ignoring additional WF restrictions in vector autoregressive modeling can be high, especially when the SC criterion is used.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cointegration; Common Cyclical Features; Reduced Rank Model; Information Criteria
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods

References

Anderson, T. W. (1951). Estimating linear restrictions on regression coefficients for multivariate normal distributions. The Annals of Mathematical Statististics, 22:327–351.

Box, G. E. & Tiao, G. C. (1977). A canonical analysis of multiple time series. Biometrika, 64:355–365.

Braun, P. A. & Mittnik, S. (1993). Misspecifications in vector autoregressions and their effects on impulse responses and variance decompositions. Journal of Econometrics, 59:319–41.

Caporale, G. M. (1997). Common features and output fluctuations in the United Kingdom. Economic Modelling, 14:1–9.

Carrasco, C. G. & Gomes, F. (2009). Evidence on common features and business cycle synchronization in Mercosur. Brazilian Review of Econometrics, 29:forthcoming.

Centoni, M., Cubadda, G., & Hecq, A. (2007). Common shocks, common dynamics and the international business cycle. Economic Modelling, 24:149–166.

Engle, R. & Granger, C. (1987). Cointegration and error correction: Representation, estimation and testing. Econometrica, 55:251–76.

Engle, R. & Issler, J. V. (1993). Common trends and common cycles in Latin America. Revista Brasileira de Economia, 47:149–176.

Engle, R. & Issler, J. V. (1995). Estimating common sectoral cycles. Journal of Monetary Economics, 35:83–113.

Engle, R. & Kozicki, S. (1993). Testing for common features. Journal of Business and Economic Statistics, 11:369–395.

Gonzalo, J. (1994). Five alternative methods of estimating long-run equilibrium. Journal of Econometrics, 60:203–233.

Guill´en, O. T. C., Issler, J. V., & Athanasopoulos, G. (2005). Forecasting accuracy and estimation uncertainty using VAR models with short-and long-term economic restrictions: A Monte-Carlo study. Ensaios Econômicos EPGE 589.

Hecq, A. (2002). Common cycles and common trends in Latin America. Medium Econometrische Toepassingen, 10:20–25.

Hecq, A. (2006). Cointegration and common cyclical features in VAR models: Comparing small sample performances of the 2-step and interative approaches. Mimeo.

Hecq, A., Palm, F. C., & Urbain, J. P. (2006). Testing for common cyclical features in VAR models with cointegration. Journal of Econometrics, 132:117–141.

Izenman, A. J. (1975). Reduced rank regression for the multivariate linear model. Journal of Multivariate Analysis, 5:248–264.

Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoegressive models. Econometrica, 59:1551–1580.

Johansen, S. (1995). Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press.

Kilian, L. (2001). Impulse response analysis in vector autoregressions with unknown lag order. Journal of Forecasting, 20:161–179.

Lutkepohl, H. (1993). Introduction to Multiple Time Series Analysis. Springer, New York.

Mamingi, N. & Iyare, S. O. (2003). Convergence and common features in international output: A case study of the economic community of West African States 1975-1997. Asian African Journal of Economics and Econometrics, 3:1–16.

Tso, M. K. (1981). Reduced rank regression and canonical analysis. Journal of the Royal Statistical Society, 43:183–189.

Vahid, F. & Engle, R. (1993). Common trends and common cycles. Journal of Applied Econometrics, 8:341–360.

Vahid, F. & Issler, J. V. (2002). The importance of common cyclical features in VAR analysis: A Monte Carlo study. Journal of Econometrics, 109:341–363.

Velu, R. P., Reinsel, G. C., & Wichern, D. W. (1986). Reduced rank models for multiple time series. Biometrika, 73:105–118.