PC-VAR Estimation of Vector Autoregressive Models

Abstract

In this paper PC-VAR estimation of vector autoregressive models (VAR) is proposed. The estimation strategy successfully lessens the curse of dimensionality affecting VAR models, when estimated using sample sizes typically available in quarterly studies. The procedure involves a dynamic regression using a subset of principal components extracted from a vector time series, and the recovery of the implied unrestricted VAR parameter estimates by solving a set of linear constraints. PC-VAR and OLS estimation of unrestricted VAR models show the same asymptotic properties. Monte Carlo results strongly support PC-VAR estimation, yielding gains, in terms of both lower bias and higher efficiency, relatively to OLS estimation of high dimensional unrestricted VAR models in small samples. Guidance for the selection of the number of components to be used in empirical studies is provided.

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C. Morana, "PC-VAR Estimation of Vector Autoregressive Models," Open Journal of Statistics, Vol. 2 No. 3, 2012, pp. 251-259. doi: 10.4236/ojs.2012.23030.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[22] M.H. Pesaran, T. Schuerman, S.M. Weiner, “Modelling Regional Interdependencies Using a Global Error Correcting Macroeconometric Model”, Journal of Business and Economic Statistics, Vol. 22, No. 2, 2004, 129-162. doi: 10.1198/073500104000000019
[23] C. Morana, “Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks”, 2011, http://ssrn.com/abstract=1756376
[24] J. Bai, “Estimating Cross-section Common Stochastic Trends in Nonstationary Panel Data”, Journal of Econometrics, Vol. 122, No. 1, 2004, pp. 137-38. doi:10.1016/j.jeconom.2003.10.022
[25] J. Bai, “Inferential Theory for Factor Models of Large Dimensions”, Econometrica, Vol. 71, No. 1, 2003, pp. 135-171. doi: 10.1111/1468-0262.00392
[26] J.R.G. Lansang, E.B. Barrios, “Principal Components Analyisis of Nonstationary Time Series Data”, Statistics and Computing, Vol. 19, No. 2, 2009, pp. 173-187. doi: 10.1007/s11222-008-9082-y
[27] C. Morana, “Oil Price Dynamics, Macro-Finance Interactions and the Role of Financial Speculation”, FEEM Working Paper Series, No. 7, 2011, http://ssrn.com/abstract=2025787

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