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Professor Salyer, Economics 200E
1
A brief introduction to discrete state Markov processes
Suppose the random variable x
t
can take on n possible values denoted xi n
i
, , , ,...,G01 123 . A
Markov process for x
t
is defined by the property:
G01G02G01G02
Pr | , , ,... Pr |xxxxxxxx xxxx
tjtitkth tjtiG01G02G02 G01
G01G01 G01 G01 G01 G01G01
112 1
.
That is, the current realization provides all the information needed for making forecasts.
For expositional purposes, we will use primarily a two-state Markov process:
Possible realizations for x
t
are:
x
x
x
where x x
t
G01G02
G03
G04
G05
1
2
12
.
The transition probabilities are denoted
G01G02
G01
ij t j t i
xxxxG01G01G01
G01
Pr |
1
and are given in matrix
notation:
(1) G06 G01
G07
G08
G09
G0A
G0B
G0C
G01G01
G01G01
11 12
21 22
(Bold print denotes either a vector or matrix.) Note that each row of the transition probability
matrix is a conditional probability distribution, hence the elements ...

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