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THE TAYLOR PROPERTY IN AR AND BILINEAR PROCESSES 29
0 3
K
0 0.3
T
Α
5
5
Α
0
1 00
Φ
Φ
11
Figure 1. Graphs for K = KX( ) (on the left) and T = TL( ) (on the right) in the cases Beta(↵,2↵) (upper surface) and Beta(↵, ↵) (lower surface), 0 < < 1, 0 < ↵ < 5.
This figure shows that the presence of the Taylor property is stronger in the case Beta(↵,2↵), corresponding to greater kurtosis of the model. In the symmetrical case, the presence of the Taylor property is very weak (the values of TBeta(↵,↵)( ) are close to zero).
In the case where "t is left-skewed distributed, we have TBeta(↵, ↵ ) ( ) < 0, 2
so the Taylor property is not present in the model. In Figure 2 we present the graphforTBeta(↵,↵)( ), 0< <1, 0<↵<5.
2
0 0
T
0.3 0
Α
Φ
Figure2. GraphforT=TBeta(↵,↵)( ),0< <1,0<↵<5. 2
5
1
