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Generalized binary vector autoregressive processes
r0
) P ( et = r0
) =
∑ r0∈{0,1}2
( 𝛽11𝛿r0,1s0,1
+ 𝛽12𝛿r0,2s0,1
)( 𝛽21𝛿r0,1s0,2
+ 𝛽22𝛿r0,2s0,2
) pr0 . (2.30)
As the distribution of Btet takes values in {0, 1}2, it is fully specified by three [...] following example.
Example 2.12 (gbVAR(2) with singular Yule–Walker matrix). Suppose (Xt, t ∈ ℤ) is a bivariate gbVAR(2) process with
1 =
( 𝛼(1)11 𝛼(1)12
1 0
) , 2 =
( 𝛼(2)11 𝛼(2)12
0 0
) , and =
( 𝛽11 [...] generate et,2 conditional on the outcome of et,1 such that P ( et,2 = 1|et,1 = 1
) = 0.9 and
P ( et,2 = 1|et,1 = 0
) = 0.2. This leads to a marginal Bernoulli distribution of et,2 with P
( et,2 = 1
) = 0 …
