Final_1.pdf

the assumption being that and are not correlated. The observa-
tion equation is given as

The variance of Ytis calculated as described in the discussion of the obser-
vation equation. We now define

The Kalman equations providing the minimum variance linear estimate are
as follows:

ˆˆ

var ˆ

var ˆ var

var ˆ var

||

|

|

|

XgX gY

X

XY

XY

tt t tt t t

tt

tt t

tt t

=+−()

()=

()()

()+ ()

−

−

−

1

1

1

1

g

Y

YX

t

t

ttt

=

()

()+ ()−

var

var var ˆ|1

YXttt=+ˆ η

Xˆ

td−− 1

Xˆ

t− 1

204 RISK ARBITRAGE PAIRS