The classic first workout of a time-series course: take a process defined by its MA(∞) coefficients and show it is an ARMA(1,1); derive means, variances and autocorrelations along the way. The set comes with tutorial questions plus video exercise sheets, and the accompanying solution notes work the recursions line by line.
What these materials cover
- MA(∞) representations and their coefficient recursions
- Showing an MA(∞) process is ARMA(1,1)
- Deriving means, variances and autocovariances
- Tutorial questions vs self-study video questions
- Two vintages of fully worked video-solution notes
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 1: exercise questions (PDF) Video-solution notes (edition 1) (PDF) Video-solution notes (edition 2) (PDF) TeX source (problem set) (.tex)
Who this is for
MSc students starting time series, and anyone practising the representation-and-moments derivations that anchor time-series exams.
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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
- AR, MA and ARMA processes explained — study note
- Time series econometrics part 2 (technical)
- All teaching materials — notes, exercises and solutions
One-to-one help
For help with this material — or the module it belongs to — see econometrics tuition or university economics tuition. The first consultation is free, with no obligation.
Free worked video lectures: @economaths on YouTube.