A Simple Test for Serial Correlation
Serial correlation is pretty easy to spot. Sometimes, lay persons who lack scientific knowledge may demand a statistical test demonstrating the
existence of unmodeled serial correlation without providing supporting data. This can be easily performed as follows under a few easily-met
assumptions.
The first assumption is that the error distribution for the model is symmetric. This is easily met if the model uses normally distributed errors or is
otherwise based on a normal distribution, as is ordinarily the case for models for continuous dependent variables. Technically, this assumption isn't
really necessary - it can also be met by, for example, log-normal models with an assymetric error distribution, but you probably shouldn't use this
test on models of integer counts.
The second assumption is that serial correlation isn't actually observed due to random chance. Admittedly, this is difficult to prove conclusively; we
would expect to see spurious results in 1/20 models which are significant at the 95% level. So it is best to use this test when you have some reason
to believe that serial correlation might actually be a factor; otherwise, you might be accused of data mining.
To do the test, simply calculate the sign of each error and then determine how many of the error signs are equal to the previous error sign in the
time series. This number is distributed according to a binomial distribution with p=0.5 and n=N-1 (where N is the number of errors in the model). It
is thus trivial to obtain a quantitative measure indicating the presence of unmodeled serial correlation of a flawed time series model without access
to the source data, merely by looking at a chart.
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