The simplest form of a white noise process is where its observations are uncorrelated. We can check this by applying e.g. a pormanteau test such as Lung - Box or Box - Pierce. The series might be Gaussian white noise where the observations are uncorrelated and also normally distributed and hence iondedpendent. We can test this with a normality test and a pormentau test. As far as i know there is a third case where the observations are uncorrelated and independent without beiing normally distribuited. In that case how can we test whether the observations are independent? Is there a statistical test for this?

Thanks in advance,

Andreas

The simplest form of a white noise process is where its observations are uncorrelated. We can check this by applying e.g. a portmanteau test such as Lung - Box or Box - Pierce. The series might be Gaussian white noise where the observations are uncorrelated and also normally distributed and hence independent. We can test this with a normality test and a portmanteau test. As far as I know there is a third case where the observations are uncorrelated and independent without being normally distributed. In that case how can we test whether the observations are independent? Is there a statistical test for this?