An ARMA model does not explain why a yield moved; it turns the information in its own past into a best linear forecast under a correctly specified stationary model. That makes it a useful benchmark: a trading signal or structural macro model must beat this disciplined use of history out of sample.
Learning objectives. By the end of this note you should be able to:
- state AR, MA, and ARMA processes using lag polynomials;
- distinguish persistence in observations from persistence in shocks;
- explain the Wold representation;
- match the model class to a forecasting question.
This note uses the stationarity, white-noise, ACF, and PACF definitions established in the previous lesson.
In this lesson
- Three representations of linear dependence
- From an ARMA equation to shock propagation
- Wold’s existence claim
- What the model class can and cannot do
- A modelling decision, not just notation
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
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