Portmanteau Test For Randomness In Poisson Data

While the use of the Portmanteau as a test for randomness in continuous data is well-known, this paper shows it can be applied it to discrete, Poisson data as well. Surprisingly, the Portmanteau test is useful even when the observed counts are small. Also surprising is the finding that small lags are more sensitive for detecting trends and transients than large lags. We show the Portmanteau is superior to the method of runs, the best previous test of randomness for discrete data. These findings allow the Portmanteau test to be used in many quality control applications (such as number of defective parts, machine breakdowns, etc.) as well as human behavior (such as issued patents or even crimes).