# When can Autocorrelation of Residuals be ignored?

One assumption of OLS regression is that residuals are idependent, so that there is no autocorrelation.

When I checked the assumption, I noticed that autocorrelation is present. Now here are two questions:

1. Is it always naccessary to remove autocorrelation? Even, when there is small autocorrelation?

2. I tried to remove autocorrelation by incorporating seasonality (i.a. dummy variables for days / months). But it didn't work. The residual plots looks exactly the same (see figure). What else can be done?

Here's a mit more information: I do not really have time series data. My data set has many observations for each point in time. For example, for the 01.01.2018 I have 5 observations with 5 different residuals. For the 02.01.2018 I have 1 observation and 1 residual. In order to detect autocorrelation, I averaged residuals for each day.

Can this be problematic? Because days with one observation are more likely to take extreme values, than averaged days with a large number of observations.

• Why you do not incorporate the auto-correlation into the model? – user158565 Dec 12 '18 at 20:29
• I incorporated dummy variables for weekdays, because significant lags tend to be multiplies of 7. However nothing has changes much. The ACF plot looks nearly the same with the same significant lags. What else can be done? – Hans Meier Ruth Dec 12 '18 at 21:22
• How about fit two models: one with auto-correlation and another without auto-correlation. Then likelihood ratio test. If really cannot find auto-corr, use the model without auto-corr to keep the model simple. – user158565 Dec 12 '18 at 21:38