A return, yield, spread, or short rate arrives in time order. Treating those observations as an iid cross-section discards the signal that a treasury desk or systematic strategy tries to trade: predictable conditional-mean dynamics. This topic supplies the disciplined workflow for modelling that signal with stationary ARMA processes. It begins with stationarity and the correlogram, builds AR, MA and mixed processes, makes the root restrictions explicit, then turns the machinery into a Box–Jenkins model-selection and forecasting routine.
By the end of this note you should be able to:
- distinguish strict and weak stationarity, and read white noise, ACF, and PACF diagnostics;
- write AR, MA, and ARMA models in lag-operator form;
- check stationarity and invertibility from characteristic roots;
- identify, estimate, diagnose, and compare candidate ARMA models;
- produce and judge one-step and multi-step forecasts.
In this lesson
- Contents
- The big picture
The full lesson is for members.
Read the full lessonNew to SelfMadeQuant.com? See membership options or browse the Econometrics and Financial Time Series syllabus.