BERND PAPE Asset Allocation, Multivariate Position Based Trading ...

48 ACTA WASAENSIAdivisible version of the TLF has been given by Koponen (1995), who considers anexponential decay rather than a discontinuous cutoff of the Lévy stable distributedprice increments. This Exponentially Truncated Lévy Flight is also contained as aspecial case of the generalization of the VG process by Carr et al. (2002) discussed insection 3.2.3.3.2.5 Comparison and EvaluationThe comparison of the suggested return distributions in the empirical finance literatureyields no coherent picture of superiority for any of the numerous candidates. This maybe partly due to the complication arising from the fact that–ecxept for the members ofthe EGB and SGT families discussed in section 3.2.4–the different distributions are notnested, making statistical inference by means of likelihood ratio tests impossible. Moststudies resort then to χ 2 goodness-of-fit tests after arranging the empirically observedreturn frequencies into class intervals and regarding the values within each intervalas a dummy class, and/or use information criteria such as the Schwartz criterion todiscriminate between the different candidates.Praetz (1972) compares the Student t with the Gaussian, Compound Events, andsymmetric stable distributions on weekly returns of Australian stocks in 1956—66 andfinds the Student t distribution to perform best in χ 2 goodness-of-fit tests. Similarly,Blattberg & Gonedes (1974) find that the Student t distribution fits daily returns betterthan the symmetric stable distribution for 30 DJI stocks in the period 1957—62; andKim & Kon (1994) find that the Student t distribution dominates both the discretemixture of normals and the compound events model in describing daily returns of 30DJI stocks and 3 stock indexes in the time period 1962—90.On the contrary, Kon (1984) claimed superiority of the discrete mixture of normalswhen comparing it to the Student t distribution on similar data, but within the shortertime interval 1962—80, and upon comparing values of their respective likelihood functions.Similarly, Gillemot, Töli, Kertesz & Kaski (2000) compare the Gaussian, thediscrete mixture of normals, jump diffusion, Student t, the stable distribution, and