eldorado.tu-dortmund.de/server/api/core/bitstreams/5fbbfb60-67b0-4c6b-9486-1afceaa37ca9/content
Generalized binary vector autoregressive processes
𝛼≠𝟙{𝛼=−𝛼≠≥0} + 𝛼=𝟙{𝛼=−𝛼≠<0} + 𝛽=𝜇𝜖
1 − |𝛼= − 𝛼≠| . (1.9)
We refer to the Supporting Information for a proof of (1.8) and (1.9). In Figure 3, we show realizations and corresponding autocorrelation [...] 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
) = 0.9 ⋅ 0.26 +
0.2 ⋅ (1 − 0.26) = 0.382. For a [...] by defining the Kp-dimensional vectors
X̃t ∶= (X′ t ,… ,X′
t−p+1) ′ and ẽt ∶= (e′t , 0,… , 0)′ (2.9)
and the (Kp × Kp)-dimensional matrices
Ã(+) t ∶=
⎛⎜⎜⎜⎜⎝ A(+,1)
t … A(+,p−1) t A(+,p)
t
IK 0K×K 0K×K …
