# Understanding the violation of the independence assumption in regression analysis of time series

I am studying time series using regression analysis. I know that when using time series data the assumption that the errors are independent cannot be satisfied.

However, analysing the residual plot: In my opinion, it does not have a positive autocorrelation because I cannot see a cyclic pattern. Also, it does not show a negative autocorrelation.

I think that there is a random pattern and it indicates that there is no autocorrelation or little autocorrelation.

I did a Durbin-Watson test to confirm the above ideas and the value for the test is 2.349. It is greater than 2 but very close to 2, so I assumed that there is no autocorrelation.

Additionally I checked that the p-values for the coefficients are very small, less than 5%. It means that they are all significant. Also, the value for the F-test and p-values shows that the model is significant

All these, show that autocorrelation is not a problem in this case and that the assumption that the errors are independent are not being violated. However I am confused because I am using time series data where I used dummy variables for seasonality and according to what I read this assumption is not satisfied when using time series but in my case I think that there is no autocorrelation.

Can anyone help me on this?

I edited my question to add the following plots of the ACF and PACF: • Did you take a look at the ACF and PACF plots of the residuals? If you can, post them. A raw plot of the residuals is not particularly helpful in identifying autocorrelation, and a plot of fitted vs residuals is not at all because there is no time ordering to the plot. – Chris Haug Mar 18 '17 at 18:06
• Hi, I added the autocorrelation plot and the Partial autocorrelation plot. I do not know how to interpret them. Can you please point me to a website where I can find more about this? So regarding what you said I cannot use the fitted values plot to see if there is or not autocorrelation? Also, the Durbin test is not enough to show that there is no autocorrelation as it is close to 2? – user290335 Mar 18 '17 at 18:19