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Maximizing Equity Market Sector Predictability in a Bayesian Time Varying Parameter Model* - page 26 / 46

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where u11 and u10 are non-informative priors and n11 and n10 are the number of transitions from state 1 to state 1 and state 1 to state zero respectively.

q ~ Beta(u00 n00 ,u01 n01 )

(A5)

where u00 and u01 are non-informative priors and n00 and n01 are the number of transitions from state zero to state zero and state zero to state 1 respectively.

The algorithm for one iteration of the Gibbs sampler for the model in (5) proceeds as follows:

(i)

2 v,

2 u

Generate T from (T |   , ST ,Y ) by running the Kalman filter described in (3), where conditional on ST , T is independent of p and q .

T

(ii)

2 u

Generate ST from (ST | , T , p,q,Y ) where conditional on T , ST is independent of .

T

2 v

(iii)

G e n e r a t e 2 k v f o r k = 1 t o 5 f r o m ) | ( , 2 T k v k w h e r e c o n d i t i o n a l o n T k , i n d e p e n d e n t o f T u Y q p , , , 2 a n d 2 j v f o r a l l k j .

,

2 vk

is

(iv)

G e n e r a t e 2 0 u f r o m ) , , , | ( 2 0 T T T u Y S h w h e r e c o n d i t i o n a l o n h , T S a n d T , 2 0 u i s i n d e p e n d e n t o f q p , a n d 2 v .

(v)

G e n e r a t e h f r o m ) , , , | ( 2 0 T T T u Y S h w h e r e c o n d i t i o n a l o n 2 0 u , T S a n d T , 2 u i s i n d e p e n d e n t o f q p , a n d 2 v .

  • (vi)

    Generate p from ( p | ST ) where conditional on ST , p is independent of all other conditioning information.

  • (vii)

    Generate q from (q | ST ) where conditional on ST , q is independent of all other conditioning information.

Here

2 v

[

2 v 1

2 v 2

2 v 3

2 v 4

2 v 5

]

and

2 u

[

2 u0

] 2 1 u .

25

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