A Simulation Study on the Performances of Classical Var and Sims-Zha Bayesian Var Models in the Presence of Autocorrelated Errors
ABSTRACT
It is well known that a high degree of positive dependency among the errors generally leads to 1) serious underestimation of standard errors for regression coefficients; 2) prediction intervals that are excessively wide. This paper set out to study the performances of classical VAR and Sims-Zha Bayesian VAR models in the presence of autocorrelated errors. Autocorrelation levels of (-0.99, -0.95, -0.9, -0.85, -0.8, 0.8, 0.85, 0.9, 0.95, 0.99) were considered for short term (T = 8, 16); medium term (T = 32, 64) and long term (T = 128, 256). The results from 10,000 simulation revealed that BVAR model with loose prior is suitable for negative autocorrelations and BVAR model with tight prior is suitable for positive autocorrelations in the short term. While for medium term, the BVAR model with loose prior is suitable for the autocorrelation levels considered except in few cases. Lastly, for long term, the classical VAR is suitable for all the autocorrelation levels considered except in some cases where the BVAR models are preferred. This work therefore concludes that the performance of the classical VAR and Sims-Zha Bayesian VAR varies in terms of the autocorrelation levels and the time series lengths.
It is well known that a high degree of positive dependency among the errors generally leads to 1) serious underestimation of standard errors for regression coefficients; 2) prediction intervals that are excessively wide. This paper set out to study the performances of classical VAR and Sims-Zha Bayesian VAR models in the presence of autocorrelated errors. Autocorrelation levels of (-0.99, -0.95, -0.9, -0.85, -0.8, 0.8, 0.85, 0.9, 0.95, 0.99) were considered for short term (T = 8, 16); medium term (T = 32, 64) and long term (T = 128, 256). The results from 10,000 simulation revealed that BVAR model with loose prior is suitable for negative autocorrelations and BVAR model with tight prior is suitable for positive autocorrelations in the short term. While for medium term, the BVAR model with loose prior is suitable for the autocorrelation levels considered except in few cases. Lastly, for long term, the classical VAR is suitable for all the autocorrelation levels considered except in some cases where the BVAR models are preferred. This work therefore concludes that the performance of the classical VAR and Sims-Zha Bayesian VAR varies in terms of the autocorrelation levels and the time series lengths.
KEYWORDS
Simulation, Performances, Vector Autoregression (VAR), Classical VAR, Sims-Zha Prior, Bayesian VAR (BVAR), Autocorrelated Errors
Simulation, Performances, Vector Autoregression (VAR), Classical VAR, Sims-Zha Prior, Bayesian VAR (BVAR), Autocorrelated Errors
Cite this paper
Adenomon, M. , Michael, V. and Evans, O. (2015) 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: 10.4236/ojmsi.2015.34016.
Adenomon, M. , Michael, V. and Evans, O. (2015) 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: 10.4236/ojmsi.2015.34016.
References
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http://dx.doi.org/10.3102/10769986021004390 [4] Gujarati, D.N. (2003) Basic Econometrics. 4th Edition, The McGraw-Hill Co., New Delhi. [5] Rao, P. and Griliches, Z. (1969) Small-Sample Properties of Several Two-Stage Regression Methods in the Context of Autocorrelated Errors. Journal of American Statistical Association, 64, 253-272.
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http://dx.doi.org/10.1111/1467-9868.00127 [8] 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, 47-53. [9] Adenomon, M.O. and Oyejola, B.A. (2015) Forecasting Bivariate Time Series with AR(1) Error Terms. A Paper Presented at the 39th Annual Conference of the Nigerian Statistical Association (NSA), Osun State, 9-11 September 2015. [10] Lutkepohl, H. and Breitung, J. (1997) Impulse Response Analysis of Vector Autoregressive Processes: System Dynamic in Economic and Financial Models. [11] Yang, M. (2002) Lag Length and Mean Break in Stationary VAR Models. The Econometrics Journal, 5, 374-386.
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http://dx.doi.org/10.1093/pan/mpp001 [15] Sims, C.A. and Zha, T. (1999) Error Bands for Impulse Responses. Econometrica, 67, 1113-1155.
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[1] Oloyede, I. and Yahya, W.B. (2015) Bayesian Generalized Least Squares with Autocorrelated Error. Book of Abstract of the 34th Annual Conference of the Nigerian Mathematical Society (NMS), 23-26 June 2015. [2] Okorie, C.E., Abubakar, U.Y and Adetutu, O.M. (2015) Analysis of Autocorrelated Data. Book of Abstract of the 34th Annual Conference of the Nigerian Mathematical Society (NMS), 23-26 June 2015. [3] Huitema, B.E., Mckean, J.W. and Zhao, J. (1996) The Runs Test for Autocorrelated Errors: Unacceptable Properties. Journal of Educational & Bahaviourial Statistics, 21, 390-404.
http://dx.doi.org/10.3102/10769986021004390 [4] Gujarati, D.N. (2003) Basic Econometrics. 4th Edition, The McGraw-Hill Co., New Delhi. [5] Rao, P. and Griliches, Z. (1969) Small-Sample Properties of Several Two-Stage Regression Methods in the Context of Autocorrelated Errors. Journal of American Statistical Association, 64, 253-272.
http://dx.doi.org/10.1080/01621459.1969.10500968 [6] Berenblut, I.I. and Webb, G.I. (1973) A New Test for Autocorrelated Errors in the Linear Regression Model. Journal of Royal Statistical Society B, 35, 33-50. [7] Smith, M., Wong, C.-M. and Kohn, R. (1998) Additive Non-Parametric Regression with Autocorrelated Errors. Journal of Royal Statistical Society B, 60, 311-331.
http://dx.doi.org/10.1111/1467-9868.00127 [8] 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, 47-53. [9] Adenomon, M.O. and Oyejola, B.A. (2015) Forecasting Bivariate Time Series with AR(1) Error Terms. A Paper Presented at the 39th Annual Conference of the Nigerian Statistical Association (NSA), Osun State, 9-11 September 2015. [10] Lutkepohl, H. and Breitung, J. (1997) Impulse Response Analysis of Vector Autoregressive Processes: System Dynamic in Economic and Financial Models. [11] Yang, M. (2002) Lag Length and Mean Break in Stationary VAR Models. The Econometrics Journal, 5, 374-386.
http://dx.doi.org/10.1111/1368-423X.00089 [12] Sims, C.A. and Zha, T. (1998) Bayesian Methods for Dynamic Multivariate Models. International Economic Review, 39, 949-968.
http://dx.doi.org/10.2307/2527347 [13] Brandt, P.T. and Freeman, J.R. (2006) Advances in Bayesian Time Series Modeling and the Study of Politics: Theory, Testing, Forecasting and Policy Analysis. Political Analysis, 14, 1-36.
http://dx.doi.org/10.1093/pan/mpi035 [14] Brandt, P.T. and Freeman, J.R. (2009) Modeling Macro-Political Dynamics. Political Analysis, 17, 113-142.
http://dx.doi.org/10.1093/pan/mpp001 [15] Sims, C.A. and Zha, T. (1999) Error Bands for Impulse Responses. Econometrica, 67, 1113-1155.
http://dx.doi.org/10.1111/1468-0262.00071 [16] Cowpertwait, P.S.P. (2006) Introductory Time Series with R. Springer Science + Business Media, LLC., New York. [17] Kadiyala, K.R. and Karlsson, S. (1997) Numerical Methods for Estimation and Inference in Bayesian VAR Models. Journal of Applied Econometrics, 12, 99-132.
http://dx.doi.org/10.1002/(SICI)1099-1255(199703)12:2<99::AID-JAE429>3.0.CO;2-A [18] Breheny, P. (2013) Wishart Priors. BST 701: Bayesian Modelling in Biostatistics.
http://web.as.uky.edu/statistics/users/pbreheny/701/S13/notes/3-28.pdf [19] Brandt, P.T., Colaresi, M. and Freeman, J.R. (2008) Dynamic of Reciprocity, Accountability and Credibility. Journal of Conflict Resolution, 52, 343-374.
http://dx.doi.org/10.1177/0022002708314221 [20] Merkin, J.H. and Needman, D.J. (1990) The Development of Travelling Waves in a Simple Isothermal Chemical System II. Cubic Autocatalysis with Quadratic and Linear Decay. Proceedings: Mathematical & Physical Sciences, 430, 315-345. [21] Merkin, J.H. and Needman, D.J. (1991) The Development of Travelling Waves in a Simple Isothermal Chemical System IV. Quadratic Autocatalysis with Quadratic Decay. Proceedings: Mathematical & Physical Sciences, 434, 531-554. [22] Worsley, K.J., Evans, A.C., Strother, S.C. and Tyler, J.L. (1991) A Linear Spatial Correlation Model with Applications to Positron Emission Tomography. Journal of the American Statistical Association, 86, 55-67.
http://dx.doi.org/10.1080/01621459.1991.10475004 [23] Caraiani, P. (2010) Forecasting Romanian GDP Using a BVAR Model. Romanian Journal of Economic Forecasting, 4, 76-87. [24] Cooray, T.M.J.A. (2008) Applied Time Series Analysis and Forecasting. Narosa Publishing House, New Delhi.