Serial independence forms the basis for classical economic and financial theories. The author contributed score tests for serial independence against alternative copula structures, leaving the marginals unspecified. Thus the score tests, which are not only invariant but also powerful against fixed alternatives under mis-specified marginals, even with the case of weak dependence, will be favorable in that the chance to commit Type I error is smaller comparing to the traditional tests. The test''s performances were numerically examined with the effects of mis-specification on both the marginals and the copula by simulation. Finally, an application of testing serial independence in log-returns of stock indices was presented. The book is written for theoretical econometricians and statisticians who has a background of dependence theory, hypothesis testing and time series analysis.