The multivariate split nomal distribution extends the usual multivariate normal distribution by a set of parameters which allows for skewness in the form of contraction/dilation along a subset of the prinicpal axis. The paper derives some properties for this distribution, including its moment...

and hence makes the test valid for any (T, N) combination. The asymptotic distributions of the tests are derived under the null and are shown to be normally distributed. Their moments for T fixed are derived analytically using Ghazal's (1994, Statistics and Probability letters 20, 313--319) ¹...

This paper gives numerical approximations of the finite sample distribution of the KPSS test statistic. We use two types of approximations depending on whether we estimate the long-run variance or not. In the known variance case we apply a very simple Laplace inversion formula, while in the...