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I have a time series of data (about 300-750 elements, depending on the sample) and a model that has some random residues. I used the Kolmogorov–Smirnov test to make sure that the normality hypothesis can't be rejected, so I assume that the residuals are normally distributed. But now I guess I should test if they are independent of each other - so that there is no autoregression? Which test should I use (preferably one that is easily implementable in java)?

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You could try Runs test for randomness. I am not familiar with Java functions. I got a link related to runs test that may useful to you. JAVA NPST. Apart from this you could do durbin-watson test or Ljung-Box portmanteau test. Most important is the visual check of time series plot ( I guess you have done this already).

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If you go with Ljung-Box, which is easy to program, you might want to check out this question and answers. – jbowman Jan 3 '12 at 17:22
Hi, which flavor of the runs test? Calculating the runs when the value increases and decreases? – Grzenio Jan 4 '12 at 13:09
You need to check both. The rejection rule is $R \leq C_1$ or $R \geq C_2$, where $C_1$ and $C_2$ are critical values obtained from table (or from normal distribution for large sample) – vinux Jan 4 '12 at 14:08
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Another option is a permutation test. Compute a measure of autocorrelation, then randomly permute the values and recompute the same measure of autocorrelation. Do the permute and recompute step a bunch of times (like 2,000 overall) and compare the value for the original ordering to the permuted values to do the test.

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