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"This simple framework provides a systematic way to capture rich dynamics in multiple time series, and the statistical toolkit that came with VARs was easy to use and to interpret. As Sims (1980) and others argued in a series of influential early papers, VARs held out the promise of providing a coherent and credible approach to data description, forecasting, structural inference and policy analysis" (Stock and Watson, 2001).
"Notwithstanding the increased use of estimated dynamic stochastic general equilibrium (DSGE) models over the last decade, structural vector autoregressive (VAR) models continue to be the workhorse of empirical macroeconomics and finance" (Kilian, 2013).
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As VAR is a multivariate model, so before departure please equip yourself with some basic weapons, including linear algebra/cookbook on linear algebra (matrix rules), concepts and definitions (e.g. lag operators and polynomials) used in time series, such as here, or here.
How to Estimate a VAR after March 2020 by Lenza, M., & Primiceri, G. E. (2020)
>>>Structural Vector Autoregressive Analysis' by Lutz Kilian and Helmut Lutkepohl (2016)<<<
Selected lecture notes on VARs from various sources
Excellent surveys by:
Stock and Watson (2001), Luetkepolh (2011), Kilian (2013), Stock's lecture (2015), Valerie A. Ramey (2016), Stock and Watson (2016)
Identifications
Following Kilian (2013) and the updated Stock's lecture (2015), pages bellow provide selected articles on:
Short-run restrictions | Long-run restrictions | Sign restrictions | Identification through Heteroskedasticity | External instruments
Combining zero and sign restriction
TVP-VAR-SV | FAVAR | MF-VAR | STVAR |MS-VAR
For those who want to learn about Bayesian econometrics, Joshua Chan kindly provides a very helpful guidance.
Barcelona Summer School Readings
Code
Matlab: code for various models: Haroon Mumtaz | Joshua Chan | Ambrogio Cesa-Bianchi |Carlo Favero| Gianni Amisano | Jouchi Nakajima | James Hamilton | Tao Zha | Chris Sims BVAR code | Dimitris Krobilis | Gary Koop | IRIS Toolbox | BEAR Toolbox | Kilian and Lutkepohl | GVAR | Vignette | Silvia Miranda-Agrippino | Empirical Macro Toolbox | Mixed Frequency State Space Models
RATS: software forum providing code, examples.
R: Var modellings; VARsignR (Estimating VARs using sign restrictions in R by Christian Danne); Bayesian Macroeconometrics in R by Keith O'Hara (pdf); BVAR; BGVAR
STATA: Panel VAR estimation (Inessa Love).
LMulTi Time Series Analysis with Java (to reproduce examples from Lütkepohl, H. (2005), New Introduction to Multiple Time Series Analysis, New York: Springer Verlag)
Eviews: Quantitative Macroeconomic Modelling with Structural Vector Autogregressions - An Eviews Implementation by S. Ouliaris, A.R. Pagan and J. Restrepo (2015). Eviews code by David Stephan for Sign restricted VAR model.
Julia: Luca Brugnolini.
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