Materials on VARs

"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

Other readings

Code