A Specification Test for Time Series Models by a Normality

A correctly specified time series model can be used to transform the data set to obtain an i.i.d. sequence of random variables, assuming that the true parameter values are known. In reality, however, one only has an estimated model and must therefore address the sampling error associated with the parameter estimates. This paper presents a new test that does not rely on specifying any specific alternative model. The test relies on a general transformation technique to turn the i.i.d. sequence into an i.i.d. sequence of standard normal random variables, and then explores both normality and independence of this transformed sequence. Specifically, we utilize the theoretical properties of the transformed random variables to construct a set of test statistics, and for all of them the sampling errors associated with any root-n consistent parameter estimates can be eliminated. The size and power of this new test are examined. We find the size of this test to be accurate for several time series models including the AR, GARCH and diffusion models. The power of this test is high in comparison to the existing tests. The test is then applied on real data series of stock returns and interest rates