Page 61 - Special Topic Session (STS) - Volume 2

STS459 Gan C.P. et al.
of the sub-table. Combining the -th sub-windows for the N companies, we

get the -th window of N  n  w 1 i w  rows.

The data for in the -th window is fitted with an [ + 3( − 1)] -

dimensional MPN distribution. From the MPN distribution for the vector of
[ + 3( − 1)] values, a large number of the values of are generated.

The components of may be divided into five groups of which group 0
consists of the value of the selected macroeconomic variable, group 1 consists
of the second till the N-th components, group (3 ≤ ≤ 5) consists of the next
− 1 components. By using the criterion based on the distance defined in
Gan and Pooi (2015), the codes for company and credit ratings are converted
to integer values. Thus the components of are transformed to the vector (1)
of which the first component gives the values of the selected macroeconomic
variable, the second component represents the index of the company, while
the last 3 components are the ratings in the previous, present and future
quarters.
From the large number of the (1) generated, we form a table consisting
of the values of (1) which correspond to a chosen company and the chosen
ratings ( () and () , say) in the previous and present quarters. We next form
a sub-table by deleting the second to fourth columns of the original table. A
row in the sub-table then gives the value of a vector (2) of which the first
component is the value of the selected macroeconomic variable and the
second component is the rating in the next quarter for the selected company
with the specified rating () in the previous quarter and the rating () in the
present quarter.
When the first value of (2) is given by the first value of the -th row of the
sub-table, a conditional distribution is obtained for the second value of (2) .
From the conditional distribution, we obtain the probability that the second

component of (2) lies in the interval :

= ( () + − 0.5, () + + 0.5], = 0, −1, +1 if () < 10,

or the interval
= ( () + − 0.5, () + + 0.5], = 0, −1, −2 if () = 10.

We may investigate the dependence of the probability on the value of

the selected macroeconomic variable given by the first component of (2) .
Instead of investigating the effects of the macroeconomic variables, one
at a time, we may summarize the effects of the 8 macroeconomic variables by
a small number of latent factors, and include the latent factors into the non-
Markovian model.
Ley be an × 1 vector consisting of the values of macroeconomic
∗

variables. A table consisting of rows may be formed such that in the table,

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