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Maximizing Equity Market Sector Predictability in a Bayesian Time Varying Parameter Model* - page 25 / 46

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Appendix A Gibbs sampling algorithm for model specified in (5)

Posterior densities of the parameters in (5) are estimated using Gibbs-sampling simulations. The p a r a m e t e r s t o b e e s t i m a t e d a r e } , , , , { 2 2 0 5 t o 1 f o r q p h u v k k , w h e r e h i s a p a r a m e t e r f o r

i d e n t i f y i n g 2 1 u s u c h t h a t ) 1 ( 2 2 0 1 h u u . G i v e n t h a t e a c h o f t h e d e n s i t y f u n c t i o n s f o r e a c h o f

the parameters directly from subscripts are distributions:

has the

a conjugate prior density, the unsolved conditional posterior distributions.

parameters of

the model can

To simplify

the notation,

dropped.

The

parameters

to

be

estimated

have

the

following

be drawn portfolio posterior

2 vk

~ InverseGamma(

a1

b1

2

,

2

)

(A1)

for k = 1 to 5

1 0 1 T a a b1 b0 (k ,T

  • k,T 1

)( k ,T

  • k ,T 1

)

where a0 and b0 are non-informative priors, k ,T is the vector of Kalman filter generated factor l o a d i n g s f o r f a c t o r l o a d i n g k f r o m ( 3 ) a n d 1 T i s t h e n u m b e r o f r o w s i n T k , .

( ~ 2 0 m a I n v e r s e G a m u

a2 2

,

b2 2

)

(A2)

2 0 2 T a a b 2 b 0 ( Z * ) ( Z *)

where a0 and b0 are non-informative priors, Z * is the vector of the state dependent disturbance

t e r m s * t z , w h e r e t t t t f r z 1 * . 2 T i s t h e s i z 1hSt e o f * Z .

h ~ InverseGamma(

a3 2

,

b3 2

)

(A3)

3 0 3 T a a b3 b0 (Z **)(Z **)

where a0 and b0 are non-informative priors, Z ** is the vector of the state dependent disturbance

terms

z

** t

,

where z

** t

t r

ft1t u 0

.

3 T

is

the

size

of

Z

**

.

p ~ Beta(u11 n11 ,u10 n10 )

(A4)

24

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