© 2012, David E. Giles
Thursday, March 15, 2012
Testing if a sample of data comes form a specific distribution is a central problem in statistics. This sort of "goodness-of-fit" testing is also important in econometrics, of course. Most goodness-of-fit tests involve "comparing" the empirical distribution function for the sample data with an hypothesized theoretical distribution. The tests rely on the Glivenko-Cantelli Theorem, which states that the maximum (vertical) "gap" between the empirical and theoretical c.d.f.'s will vanish, everywhere on the support of the distribution, as the sample size grows without limit.
Some such tests are based on this "maximum gap", while others are based on the area between the empirical and theoretical c.d.f.'s. Examples of the first type of test include those associated with the names of Kolmogorov, Smirnov, Kuiper, Watson and Lilliefors. Examples of the second type include the tests of Anderson and Darling, and Cramér and von Mises.
All of these tests are available in EViews. You select the series and then choose "View", "Descriptive Statistics & Tests", and then "Empirical Distribution Tests".