Detecting Asymmetries in Observed Linear Time Series and Unobserved Disturbances

Abstract

Abstract. This paper investigates the problem of testing for the symmetry of linear time series driven by asymmetric innovations. In particular, we examine the performance of alternative symmetry tests when innovations are fat tailed. Among the tests considered, only the test based on the tail estimator of the spectral measure yields satisfactory results in the presence of fat-tailed innovations.

Testing for Symmetry in Weakly Dependent Time Series

“…Although, as the number of observations grows, the performance of the symmetry test improves as would be expected. The notable loss in power of the symmetry test for very persistent processes is something which has been previously highlighted in the literature (see Kim et al 1996, Bai and Ng 2001, and Bai and Ng 2005. Indeed, Bai and Ng (2001) noted that with an ARMA model even if the innovation term t is asymmetric, it does not necessarily imply that the process y t will also be asymmetric as well.…”

Exact inference and optimal invariant estimation for the stability parameter of symmetric α-stable distributions

“…r.v.s proved by Zolotarev (1986). For more details on the α-stable distributions, see Zolotarev (1986) and Samorodnitsky and Taqqu (1994); and for a discussion of the role of the α-stable distributions in financial markets and macroeconomic modelling, see McCulloch (1996), Kim et al (1997) and Rachev et al (1999).…”

“…(4) The size distortion is more dramatic as α approaches 2, because the thinner the tail becomes, the more difficult to estimate it precisely, and it is well known that the Hill-type estimates have a bias as α approaches 2. This phenomenon has a severe consequence in empirical studies, because most empirical data have an α between 1.5 and 2 (see Kim et al, 1997) meaning that a careful choice of k, or rather, using a method without assuming known k, is of importance for empirical work. The results of the asymptotic test show that it suffers generally from size distortion, even for the known case if α is small.…”

The Performance Of Nonlinearity Tests On Asymmetric Nonlinear Time Series

“…Finally, we will summarize the findings and discuss the potential implications and avenues for future work. Kim and Mittnik (1996) discussed the asymmetric data generating process (DGP):…”