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I have annual data consisting of twenty datapoints (I know not a lot) and I want to check the residuals of a linear model for autocorrelation.

The ACF plot does not show peaks outside the confidence limits, however the DW-test does reject no-autocorrelation (DW = 1.3789, p-value = 0.03063).

When I do a runstest, it cannot reject the null hypothesis that the sequence is random (therefore indicates no autocorrelation).

The Breusch-Godfrey test rejects no autocorrelation for all lags except lag=2.

My question is now which approach is the most reliable, and why the DW-test contradicts the ACF plot (and also why the BG test rejects only for lag 2, but not for larger or smaller order, although this might be a different story).

EDIT: now I ran in a different case in which the BG test rejects no autocorrelation (at all lags except lag=1), while the ACF plot shows no peaks crossing the limits. The DW test shows: DW = 1.4694, p-value = 0.05063 and the runs test has a p-value of 0.06 (indicating randomness). So now I am wondering why the BG tests rejects while the ACF shows no correlation.

Thanks in advance!

ACF plot

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