Autocorrelation
The correlation of a series, or of a model's residuals, with its own past values at a given lag. Significant residual autocorrelations show a time-series model is misspecified.
Where you will meet it
Autocorrelation appears in 4 learning outcomes on the CFA syllabus. A few of them:
- Explain how residual autocorrelations let you check whether an autoregressive model suits a time series
“To check that an AR model is correctly specified, examine the autocorrelations of its residuals rather than a Durbin–Watson statistic, which is invalid when a lagged dependent variable is a regressor.”
- Explain how to detect and adjust for seasonal effects in a time-series model, and work out and explain a forecast from an AR model that includes a seasonal lag
“Seasonality shows up as a significant residual autocorrelation at the seasonal lag, four for quarterly data and twelve for monthly data, after an AR model is fitted.”
- Say what autoregressive conditional heteroskedasticity (ARCH) is and show how ARCH models help forecast a time series' variance
“Common slips are to use the unsquared residual, or to assume that no autocorrelation in the residuals rules out ARCH.”
- Choose a suitable time-series model for a given investment problem and give reasons for the choice
“Fit an AR(1) and test the residual autocorrelations, adding lags or a seasonal lag until none is significant.”
See also
Correlation · Misspecification
Practise it
Practise autocorrelation until it is automatic: questions that explain every wrong option.
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