Diagnosing Residual Autocorrelation in an AR Model
Summary
The document considers an operating-margin time series initially modeled as an autoregression of order one. Adding a fourth-lag term reduces the residual autocorrelation at that lag, but the remaining test statistic is still slightly above two and the added coefficient appears insignificant. The responses suggest checking whether the series has seasonal structure and whether differencing or other stationarity adjustments are needed before choosing an ARIMA specification.
For model selection, they recommend inspecting the autocorrelation and partial autocorrelation patterns, using information criteria to compare candidate lag orders, and checking that fitted residuals behave like white noise. One response also raises ARCH or GARCH models as a possible direction. These are suggestions rather than a worked analysis: the document gives no data, diagnostic plots, fitted alternatives, or evidence that any proposed model improves the fit. The appropriate specification therefore remains unresolved.
Key ideas
- Check for seasonal patterns before interpreting residual autocorrelation as evidence for another autoregressive lag.
- Use autocorrelation and partial autocorrelation plots to guide AR and MA order choices.
- Confirm stationarity before fitting an ARIMA model, applying differencing when appropriate.
- Compare candidate specifications with information criteria and inspect whether residuals resemble white noise.
- ARCH or GARCH may be relevant when the series shows conditional volatility patterns.
Tags
Full text
# residual correlation remains after seasonal lag added # residual correlation remains after seasonal lag added I'm attempting to model operating margins and a time plot indicated that the series may follow an autoregressive process. I initially fitted data to an AR(1) model and it appeared that residual correlation was present in the 4th lag term. I added an additional 4th lag and while the AC in the fourth residual did decrease, the t-stat is still slightly greater than 2. Additionally, the second (4th lagged regressor) appears to be highly insignificant. I'm looking for suggestions as to how to improve on the model specification. ## Answer by Richi Wa (score 1) https://quant.stackexchange.com/a/24814 what you should analyze: - Look at seasonalities as user Horeseless points out. - Look at ACF, if it cuts off suddenly then there is something of MA nature, if it decays slowly then it is rather AR. - Look at partial ACF to see which lags are relevant. You find theory and code here. ## Answer by Neeraj (score 0) https://quant.stackexchange.com/a/28004 Before fitting any ARIMA model, make sure that: - There is no seasonal trend in your data. If it is present then deseasonalized it by taking appropriate lag difference, as pointed by @Horseless - Before fitting any model, make sure data is stationary. - Once stationarity is achieved, plot ACF and PACF and find appropriate lag. To find appropriate lag selection, you can use various information criterion, like AIC, BIC, SIC, HQIC etc. (Lot of R packages are available that allow automatic selection of appropriate lag order) After fitting appropriate model, make sure that error terms (residuals) are white noise. ## Answer by UtdMan (score -1) https://quant.stackexchange.com/a/24770 you should look arch/garch models
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