Saddlepoint approximation methods for testing of serial correlation in panel time series data

The empirical saddlepoint method applied to testing for serial correlation in panel time series data

“…Next we compare the performance of the empirical saddlepoint method to that of the saddlepoint method based on the normal error assumption discussed in Perera et al (2006) when the classical normal error assumption holds. Table 3 gives the standard deviations of the differences between the p-values of the test H 0 : α = 0 against H 1 : α > 0 obtained under the theoretical saddlepoint method and the empirical saddlepoint method.…”

“…The application of the saddlepoint approximation approach to estimating the p-value for testing for serial correlation for the normal error, equal variance version of this model with equal series lengths was discussed in Perera et al (2006). In the current context the saddlepoint approximation is used to approximate the cumulative distribution function of the values of the statistic S * r given the data.…”

“…, r i , where for each i, the e it are independent and identically distributed, zero mean random variables with Var(e it ) = σ 2 i . Nerlove (1967Nerlove ( , 1971, Azzalini (1981), Cox and Solomon (1988), Hjellvik and Tjostheim (1999) and Perera et al (2006) consider the above model or a slight variation of it, with the errors {e it } taken to be normally distributed, N(0, σ 2 ). The normal error, equal variance model is a very limiting assumption when considering real life situations where we might have to deal with errors that are either normal but have unequal variances across subjects, or with error structures that are non-normal.…”