My sample size is just 15. I have a Durbin-Watson statistic of 2.601 which may indicate negative autocorrelation.
First off, can I still use multiple regression analysis given the possibility that there may not be independence of observations?
Also, what does having a negative autocorrelation mean in relation to the data?
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First off, this is a very small sample, and thefore you should not try large models on it and be cautious about interpretation of results.
Do you have the critical values to compare 2.601 to? They depend on model specification, and there is not enough information in your post to identify that. You should be able to find the relevant critical values either in your programme output or by searching for "Durbin Watson critical values" online.
If 2.601 appears not to be significantly different from 2 (which it should be under the null), then you could think this is due to chance and ignore it. If 2.601 appears to be significantly different from 2, then your model is misspecified (violation of i.i.d. errors) and OLS estimators will not have all the nice properties they otherwise would.
Also, be careful with independence: it's not independence of observations but independence of errors that is relevant for OLS estimation.
A negative autocorrelation in model errors means your model is misspecified. Perhaps a variable is missing (e.g. lag of the dependent variable).
answered Nov 8, 2015 at 11:56
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$\begingroup$ To Richard Hardy's point, with only 15 observations you will not be able to fit models such as ARIMA, Box-Jenkins or VAR. After finding the critical pseudo-F value for your model -- the DW tables are readily available online or in many texts -- you fine that the errors are autocorrelated, then your next step should be to take the first difference of your response variable and re-estimate. If your data is quarterly, in theory at least, you could test for seasonality. How many predictors do you have? This will limit model fitting as you can easily and quickly exhaust the degrees of freedom $\endgroup$ Commented Nov 8, 2015 at 12:52
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$\begingroup$ @DJohnson, why difference? Differencing should be justified by a unit-root test, not by Durbin-Watson statistic. These are two different things. A stationary, non-unit-root series may have a Durbin-Watson statistic far away from 2. $\endgroup$ Commented Nov 8, 2015 at 19:06
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$\begingroup$ I assumed that first differences were a solution for autocorrelated errors. Based on your comment, it sounds like that was wrong. Tell me something, is a unit-root test even possible with 15 observations? In theory it is, but would it be a reliable test with so little information? $\endgroup$ Commented Nov 8, 2015 at 19:19
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$\begingroup$ I don't know how a unit-root test (say, the ADF test) would perform in such a small sample, but as you say, perhaps not very good. However, differencing is only a solution against a unit root, but not against autocorrelation in general. Overdifferencing (differencing when there is no unit root) brings new problems. Meanwhile, autocorrelation can be dealt with by changing the model specification or allowing the model errors to follow and ARMA pattern. $\endgroup$ Commented Nov 8, 2015 at 19:35
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$\begingroup$ But wouldn't an ARMA pattern be too data intensive in this case with only 15 obs? $\endgroup$ Commented Nov 8, 2015 at 19:42