Two noise magnitudes of loglinear noise were chosen here. Loglinear-1 with α = 0.85 and β = -1.70 follows an empirical setting suggested by Albert and Horwitz and Loglinear-2 with α = 1.20 and β = -1.30 was chosen to be a larger noise magnitudes. Parameters of noise settings can be found in Table , an illustration of different noise structures and magnitude can be found in Appendix D.