Selecting and Diagnosing ARMA Models for Financial Returns
Summary
The article explains how ARMA(p,q) combines autoregressive effects from past observations with moving-average effects from past shocks. It introduces BIC as a more severe penalty for model complexity than AIC, and the Ljung–Box test as a check of residual autocorrelation across a group of lags. It also notes that ARMA captures linear dependence but does not model volatility clustering.
Examples simulate ARMA(1,1) and ARMA(2,2) series, fit the known orders, and compare estimated coefficients with their true values; the second example shows that estimates can miss the generating parameters even in simulated data. For model selection, the article searches candidate orders using AIC, then checks residuals with the Ljung–Box test. Applied to S&P 500 daily log returns, this process selects ARMA(3,3), but the residual test indicates remaining serial dependence. The article cautions that ARMA models generally fit equity returns poorly and points toward combining ARIMA with GARCH to address conditional heteroscedasticity.
Key ideas
- ARMA models combine autoregressive terms and moving-average terms to represent dependence on past values and shocks.
- BIC penalizes additional model parameters more strongly than AIC.
- The Ljung–Box test assesses whether residual autocorrelation across a chosen set of lags remains significant.
- Choosing orders by AIC should be followed by residual diagnostics rather than treated as proof of a good fit.
- ARMA alone does not capture volatility clustering, which is common in financial returns.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.