||Many time series models have been extensively used in modelling economic and financial data. However, it is difficult to determine the functional forms of the conditional means and conditional variances in these models. In this thesis, a test statistic based on the squared conditional residuals (εt2/ht) is proposed for testing these functional forms, and its asymptotic distribution is obtained. The test statistic is applicable not only in the family of GARCH models but also in other non-linear time series models. Simulation results show that the proposed tests are powerful and have reasonable sizes. Two real examples are also given to illustrate our theory and methods.