This problem set works with a concrete bivariate VAR(1) system: given the coefficient matrix, verify whether the process is weakly stationary via the roots of the lag polynomial, and analyse the system's dynamics. The solutions file carries every matrix calculation through in full — the exact skill VAR exam questions test.
What these materials cover
- Bivariate VAR(1) systems and vector white noise
- Writing the VAR with the lag operator: Φ(L) = I − Φ₁L
- Checking weak stationarity from the roots of |Φ(z)| = 0
- Dynamics and cross-variable feedback in VAR systems
- Complete worked solutions with TeX source
Download
Free to download and use for personal study. Written for my own university teaching; shared here as evidence of teaching style and depth.
Problem set: VAR systems (2021 edition) (PDF) Full worked solutions (PDF) TeX source (solutions) (.tex)
Who this is for
MSc students taking multivariate time series, and dissertation students using VARs for macro or financial data.
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Send the module topic list, the problem set and where you're stuck. A free consultation diagnoses whether the difficulty is definitions, derivations or software output — and proposes a plan.
Related free resources
- Time Series Econometrics — full study-note hub
- Vector autoregression (VAR) basics — study note
- Time series econometrics part 2 (technical)
- All teaching materials — notes, exercises and solutions
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Free worked video lectures: @economaths on YouTube.