Considering that the character of Paul in Willa Cather's Paul's Case is, as the whole title states A Study in Temperament, it is implied that his behavior has either changed all of a sudden, or has changed and remained in a certain manner. This manner is what serves as the focus of the study.
We know that Paul is a misfit. He cannot adapt to his surroundings and has lived his life in denial of his reality. The story does not readily tell us when exactly Paul's dissatisfaction with life begins, but it is arguable that this is a gradual change that only gets more and more intense. So intense, indeed, that it ends with Paul's suicide.
This being said, Paul arguably is a dynamic character because he changes with his circumstances. Since Paul's case is so unique, however, we can see that the changes occur within a very defined scenario from Cordelia Street to the Waldorf Astoria: The transformation from Paul, the private school boy, into Paul, the dandy.