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I have calculated a Durbin-Watson test and got as far as

$$\eqalign{ d&=2.207551844, \\ dL&= 1.6164, \\ dU&= 1.7896. }$$

I want to test

$$H_0 \gt 0,\ H_1 \le 0.$$

However, I do not really know if I can reject $H_0$. What would happen if $H_0 \lt 0, H_1 \ge 0$?

Please give me a hint on the interpretation of such a test!

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In general, a test of autocorrelation would be $H_o: \rho = 0$, $H_a: \rho > 0$. (Many economic time series have positive autocorrelation, so often just the one-sided test is done when working with economic data) Why are you trying to test if the autocorrelation is either more or less than zero? What is the data that you are working with? Are you actually trying to do a two sided test of $H_o: \rho = 0$ vs. $H_a: \rho \neq 0$?? – Eric Peterson May 22 '13 at 19:28
the data are the residuals of a regression model. At the moment I am doing example from a workbook and thats the specification of it... – Le Max May 22 '13 at 20:07
up vote 3 down vote accepted

And do you have reason to believe that this data would show positive or negative autocorrelation? i.e. do you need to do a one or two sided test? Often a two sided DW test is simply carried out as two one sided tests and the $\alpha$ (type I error) for the two sided is simply doubled. So for example for the test:

$H_o: \rho = 0$

$H_a: \rho \neq 0$

Decision rule is as follows:

$If DW(2.207) > dU \rightarrow Fail\ to\ Reject\ H_o$

$If DW(2.207) < dL \rightarrow Reject\ H_o$

$if dL < DW < dU \rightarrow Test\ is\ inconclusive$

that would test for $\rho > 0$. For $\rho < 0$ the test is 4-DW (2.207), everything else is similar (e.g. if $4-DW < dL \rightarrow conclude\ \rho < 0$) But like I said above, since you've carried these two tests out seperately, if you've tested them both at the $\alpha = 0.05$ level, then you don't have the two sided test at that level. You've got the test at the $2\alpha$ level. So change your $\alpha$ level accordingly to get the desired result.

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