262 MONITORING COVARIANCES OF ASSET RETURNS

Here we have applied Theorem 3.2.14 of Muirhead (1982), for example the fact thattii
andtijare mutually independently distributed. Similar calculations lead to:

fij=

∑i

l= 1

∑j

k= 1

E(til)wlkE(tjk)=wijE(tii)E(tjj)

= 2 wij



(n−p+q−i+ 1 + 1

2

)



(n−p+q−i+ 1

2

)



(n−p+q−j+ 1 + 1

2

)



(n−p+q−j+ 1

2

)

Thus

E(cc′)=Var(c)+E(c)E(c)′=I+H ̃( 22 −) ̃b−

(^12)
Gb ̃−
12 ′
(13.23)
As a result
Var(v ̃ˆ)=E(v ̃ˆvˆ ̃′)−E(ˆ ̃v)E(vˆ ̃)′

(n−p)
2



(n−p
2 −^1
)

(n−p
2
) (I+H ̃( 22 −)b ̃−^12 Gb ̃−^12
′
)

• 
  
  
  (n−p− 1
  2
  )
  
  (n−p
  2
  )
  
  
  2
  H ̃( 22 −) ̃b−^12 F ̃b−^12
  ′
  
  
  
  The proof is complete.

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