AR Models, Stationarity, and AIC for Financial Time Series
Summary
This article introduces strict stationarity and the Akaike information criterion (AIC) before explaining autoregressive models of order p. An AR model predicts a series from its own prior values and a white-noise term, extending the random-walk idea. For an AR process, stationarity depends on its coefficients: the roots of its characteristic equation must lie outside the unit circle. AIC offers a way to compare candidate models by balancing fit against the number of parameters.
The financial examples use differenced log prices for individual equities and the S&P 500. The article describes correlograms and an automatically selected AR(22) fit for the index returns, interpreting the remaining serial correlation and changing volatility as signs that a simple AR model is insufficient. These examples motivate later consideration of MA, ARMA, ARIMA, and GARCH methods. The discussion is introductory: the article previews a model-selection approach and empirical patterns, but does not establish that the forecasts are profitable or fully address volatility clustering.
Key ideas
- An AR(p) model predicts a time-series value from a weighted combination of its previous p values and a noise term.
- An AR process is stationary only when all roots of its characteristic equation have absolute values greater than one.
- AIC compares candidate models by weighing their fit against their parameter counts.
- Correlograms of financial returns can reveal serial dependence that a basic AR model may not capture.
- Time-varying volatility limits AR models and motivates models such as GARCH.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.