Vector autoregressive (VAR) processes are popular in economics and other sciences because they are flexible and simple models for multivariate time series data. In econometrics they became standard tools when Sims (1980) questioned the way classical simultaneous equations models were specified and identified and advocated VAR models as alternatives. A textbook treatment of these models with details on the issues mentioned in the following introductory exposition is available in Lütkepohl (2005).
The Model Setup
The basic form of a VAR process is
where y t = (y 1t , …, y Kt )′ (the prime denotes the transpose) is a vector of K observed time series variables, d t is a vector of deterministic terms such as a constant, a linear trend and/or seasonal dummy variables, D is the associated parameter matrix, the A i ’s are (K ×K) parameter matrices attached to the lagged values of y t , pis the lag order or VAR...
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References and Further Reading
Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov B, Csáki F (eds) 2nd International Symposium on Information Theory, Académiai Kiadó, Budapest, pp 267–281
Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37:424–438
Hannan EJ, Deistler M (1988) The statistical theory of linear systems. Wiley, New York
Johansen S (1995) Likelihood-based inference in cointegrated vector autoregressive models. Oxford University Press, Oxford
Lütkepohl H (2005) New introduction to multiple time series analysis. Springer-Verlag, Berlin
Sims CA (1980) Macroeconomics and reality. Econometrica 48:1–48
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Lütkepohl, H. (2011). Vector Autoregressive Models. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_609
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