Performance of vector autoregressive models influenced by collinearity and autocorrelated error

The goal of Vector Autoregression (VAR) or Bayesian Vector Autoregression (BVAR) is the characterization of the dynamics and endogenous relationships among time series. The VAR models are known for their applications to forecasting and policy analysis. This paper compares the performance of VAR and Sims-Zha Bayesian VAR models when the multiple time series are jointly influenced by different levels of collinearity and autocorrelation in the short term. Simulations on different levels of collinearity and autocorrelation were performed (viz. -0.9, -0.5, 0, +0.5, +0.9). The results revealed that the VAR(2) model dominated for levels (-0.5, 0, +0.5) of autocorrelation irrespective of the collinearity level, except when T=16. The BVAR model dominated for levels (-0.9, +0.9) of autocorrelation regardless of the collinearity level, except when T=128. The forecasting models were found to depend on the Time Series data structure and the time series length.

 

Adenomon, M.O., Michael, V.A., Evans, P.O. (2015a). A Simulation Study on the Performances of Classical VAR and Sims-Zha Bayesian VAR Models in the presence of autocorrelated errors, Open Journal of Modelling and Simulation, 3, 146-158. DOI: http://dx.doi.org/10.4236/ojmsi.2015.34016.

Adenomon, M.O., Michael, V.A., Evans, P.O. (2015b). On the Performances of Some Sims-Zha Bayesian Model with Quadratic Decay for a Stable Data Generation Process, Nigeria Journal of Applied Arts and Sciences, 8, 131-140.

Adenomon, M.O., Michael, V.A., Evans, P.O. (2015c). Short Term Forecasting Performances of Classical and Sims-Zha Bayesian VAR Models for Time Series with Collinear Variables and Correlated Error Term, Open Journal of Statistics, 5, 742-753. DOI: http://dx.doi.org/10.4236/ojs.2015.57074

Adenomon, M.O., Michael, V.A., Evans, P.O. (2016). On the Performances of Classical VAR and Sims-Zha Bayesian VAR Models in the Presence of Collinearity and Autocorrelated Error Terms, Open Journal of Statistics, 6, 96-132. DOI: http://dx.doi.org/10.4236/ojs.2016.61012

Adenomon, M.O., Oyejola, B.A. (2014). Forecasting Multiple Time Series with Reduced Form Vector Autoregression (VAR) and Sims-Zha Bayesian VAR when the Endogenous Variables are Collinear, Book of Abstract of the 33rd Annual Conference of the Nigerian Mathematical Society. May, 27-30, P.46.

Brandt, P.T. (2012). Markov-Switching, Bayesian Vector Autoregression Models-Package ‘MSBVAR’. The R Foundation for Statistical Computing

Brandt, P.T., Colaresi, M. and Freeman, J.R. (2008). Dynamic of Reciprocity, Accountability and Credibility, Journal of Conflict Resolution, 52, 343-374. DOI:http://dx.doi.org/10.1177/0022002708314221

Brandt, P.T., Freeman, J.R. (2006). Advances in Bayesian Time Series Modeling and the Study of Politics: Theory, Testing, Forecasting and Policy Analysis, Political Analysis, 14(1), 1-36.

Brandt, P.T. and Freeman, J.R. (2009). Modeling Macro-Political Dynamics, Political Analysis, 17(2), 113-142

Brandt, P.T. and Williams, J.T. (2007). Multiple Time Series Models, Sage Publication Inc., USA.

Breheny, P. (2013). Wishart Priors, BST 701: Bayesian Modelling in Biostatistics.Web.as.uky.edu/statistics/users/pbreheny/701/S13/notes/3-28.

Canova, F. (1992). An Alternative Approach to Modelling and Forecasting Seasonal Time Series, Journal of Business and Economic Statistics, 10(1), 97-108.

Caraiani, P. (2010). Forecasting Romanian GDP using A BVAR model, Romanian Journal of Economic Forecasting, 4, 76-87

Carsey, T. and Harden, J. (2011). Monte Carlo Simulation and Resampling, ICPSR Summer Course.

Chama-Chiliba, M.C., Gupta, R., Nkambule, W. and Tlotleg, N. (2012). Forecasting Key Macroenomic Variable of the South African Economy Using Bayesian Variable Selection, Journal of Applied Sciences, 12(7), 645-652.

Cooray, T.M.J.A. (2008). Applied Time series Analysis and Forecasting, Narosa Publising House, New Delhi.

Cottet, R. and Smith, M. (2003). Bayesian Modelling and Forecasting of Intraday Electricity Load, Journal of the American Statistical Association, 98(464), 839-849.

Cowpertwait, P.S.P. (2006). Introductory Time Series with R, Springer Science+Business Media, LLC, New York.

Dahem, A. (2016): Short-term Bayesian Inflation Forecasting for Tunisia: Some Empirical Evidence, Ecoforum. 5(1):308-319.

Diebold, F.X. and Mariano, R.S. (2002). Comparing Predictive Accuracy, Journal of Business and Economic Statistics, 20(1), 134-144.

Dormann, C.F., Elith, J., Bacher, S., Bachmann, C., Carl, G., Lagourcade, B., Leifao, P. J., Munkemiller, T., McClean, C., Osborne, P. E., Reineking, B., Schroder, B.,Skidmore, A.K., Jurell, D. and Lautenbach, S. (2013). Collinearity: A Review of Methods to Deal with It and A Simulation Study Evaluating their Performance, Ecography, 36, 027- 046.

Dua, P. and Ranjan, R. (2011). Modelling and Forecasting the Indian Re/US Dollar Exchange Rate. Centre for Development Economics, Working Paper No. 197.

Garba, M.K., Oyejola, B.A. and Yahya, W.B. (2013). Investigations of Certain Estimators for Modelling Panel Data Under Violations of some Basic Assumptions, Mathematical Theory and Modeling. 3(10):47-53.

Giannini, C. and Mosconi, R. (1987). Predictions from Unrestricted and Restricted VAR Models, Giornale degli Economisti e Annali di Economia, Nuova Serie. 46(5/6):291-316.

Gilbert, P. (2009). Brief User’s Guide: Dynamic Systems Estimation (DSE), www.bankbanque.canada.ca/pgilbert.

Gujarati, D.N. (2003). Basic Econometrics (4th Ed), The McGraw-Hill Co., New Delhi.

Gupta, R. and Kabundi, A. (2009). Forecasting Macroeconomic Variables Using Large Data Sets: Dynamic Factor Model Versus Large-Scale BVARs. University of Pretoria & University of Johannesburg, Working Paper No. 143.

Hamilton, J.D. (1994). Time Series Analysis, Princeton University Press, Princeton.

Ijomah, M.A. and Nduka, E.C. (2010). Selection in a Multicollinear Data Using Information Criteria, Journal of the Nig. Stat. Assoc, 22, 64-75.

Kadiyala, K.R. and Karlsson, S. (1997). Numerical Methods for Estimation and Inference in Bayesian VAR Models, Journal of Applied Econometrics, 12(2), 99-132.

Leeper, E.M, Sims, C.A. and Zha, T. (1996). What Does Monetary Policy Do? Brookings Papers on Economic Activity, 27, 1-79.

Litterman, R.B. (1986a). Forecasting with Bayesian Vector Autoregressions: Five Years of Experience, Journal of Business and Economic Statistics, 4, 35-52.

Litterman, R.B. (1986b). A Statistical Approach to Economic Forecasting, Journal of Business and Economic Statistics, 4(1), 1-4.

Lűtkepohl, H. (2005), New Introduction to Multiple Time Series Analysis, Springer Berlin Heidelberg.

Lűtkepohl, H. and Breitung, J. (1997). Impulse Response Analysis of Vector Autoregressive Processes, System Dynamic in Economic and Financial Models, Ftb://Amadeus.wiwi.huberlin.de/pub/papers/sfb373/sfb1996/dpsfb960086. ps.t.

McNelis, P.D., Neftci, S.N. (2006). Renminbi Revaluation, Euro Appreciation and Chinese Market: What can we Learn from Data. HKIMR, Working Paper No. 1/2006.

Ni, S. and Sun, D. (2005): Bayesian Estimates for Vector Autoregressive Models, Journal of Business & Economic Statistics, 23 (1),105-117.

Ni, S., Sun, D. & Sun, X. (2007). Intrinsic Bayesian Estimation of Vector Autoregression Impulse Responses, Journal of Business & Economic Statistics, 25(2), 163-176.

Njenga, C.N. and Sherris, M. (2011). Modeling Mortality with Bayesian Vector Autoregression, Autralian School of Business Research Paper, No. 2011ACTL04.

Olubusoye O.E. and Okewole D.M. (2013). Bayesian Estimation of an Over-Identified Multi- Equation Model in the Presence of Multicollinearity, Journal of Nig. Stat. Assoc, 25, 93 – 109.

Paccagnini, A. (2012). Comparing Hybrid DSGE Models. Department of Economics, University of Milan-Bicocca, Working Paper Series No. 228.

Park, T. (1990), Forecast Evaluation for Multivariate Time Series Models: The US Cattle Market, Western Journal of Agricultural Economies, 15(1), 133-143.

Partridge, M.D. and Rickman, D.S. (1998). Generalizing the Bayesian Vector Autoregression Approach for Regional Inter-Industrial Employment Forecasting, Journal of Business & Economic, 16(1), 62-72.

Pfaff, B. (2008a). Analysis of Integrated and Cointegrated Time Series with R, Springer Science+Business Media, LLC, USA.

Pfaff, B. (2008b). VAR, SVAR and SVEC Models: Implementation within R Package Vars, Journal of Statistical Software, 27(4),1-32.

Phillips, P.C.B. and Ploberger, W. (1996). Asymptotic Theory of Bayesian Inference for Time Series, Econometrica, 64(2), 381-412.

Sacakli-Sacildi, I. (2015): Do BVAR Models Forecast Turkish GDP Better Than UVAR Models? British J. Econs, Mgt & Trade, 7(4), 259-268.

Shoesmith, G.L. and Pinder, J.P. (2001). Potential Inventory Cost Reductions using Advanced Time Series Forecasting Techniques, The Journal of the Operational Research Society, 52(11), 1267-1275.

Sims, C.A. (1980). Macro-Economics and Reality, Econometrica. 48, 1-48.

Sims, C.A. (2002), The Role of Models and Probabilities in the Monetary Policy Process. Brookings Papers on Economic Activity, 2002(2), 1-40.

Sims, C.A. and Zha T. (1999). Error Bands for Impulse Responses, Econometrica, 67(5), 113-1155.

Sims, C.A. and Zha, T. (1998). Bayesian Methods for Dynamic Multivariate Models, International Economic Review, 39(4), 949-968.

Smith, M., Wong, C.-M. and Kohn, R. (1998). Additive Non-Parametric Regression with Autocorrelated Errors, Journal of Royal Stat. Soc. B, 60(2), 311-331.

Suppes, P. (2007). Where Do Bayesian Prior Come From? Synthese, 156(3), 441-471.

Tahir, M.A. (2014). Analyzing and Forecasting Output Gap and Inflation Using Bayesian Vector Autoregression (BVAR) Method, A Case of Pakistan. Int. J. Econs. & Fin. 6(6), 257-266.

Uhlig, H. (1997). Bayesian Vector Autoregressions with Stochastic Volatility, Econometrica 65(1), 59-73.

Zeller, A. (1962). An Efficient Method of Estimating Seemingly Unrelated Regression and Tests for Aggregation Bias, Journal of the American Statistical Association, 57(298), 348-368.