Having defined ARMA processes, this lecture shows how to estimate them and do inference. It develops the sampling properties of the sample autocorrelation function (the basis for reading a correlogram), then builds maximum likelihood estimation of ARMA processes, connecting estimation theory to what software actually reports.
What these materials cover
- Sample moments and their large-sample behaviour
- Statistical properties of the sample ACF; correlogram confidence bands
- Maximum likelihood estimation of ARMA processes
- Inference on ARMA coefficients
- TeX source available for the full deck
Download
Free to download and use for personal study. Written for my own university teaching; shared here as evidence of teaching style and depth.
Lecture slides: estimation & inference for ARMA (2021 edition) (PDF) TeX source (.tex)
Who this is for
MSc and PhD students estimating time-series models, and dissertation students interpreting ARMA output from Stata, R or EViews.
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Related free resources
- Time Series Econometrics — full study-note hub
- ARMA estimation and model selection — study note
- How to read a correlogram — study note
- Maximum likelihood estimation explained
- All teaching materials — notes, exercises and solutions
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