Modelling the accruals process and assessing unexpected accruals*

Appendix 3: Correlation between Abnormal and Normal Accruals
If growth is assumed to grow at a constant rate g as follows
This implies the following
1
u, t u, t1
CNI g CNI
(29)
u, t u, t1 u, t1 u, t
CNI CNI g CNI g CNI
u, t1 u, t1
cov g CNI , g 1 g CNI
2 ut , 1
g 1 g var CNI
cov , cov ,
u, t u, t1
CNI g CNI
2 ut , 1
g var CNI
var var
u, t1 CNI g u, t1
g CNI
2 2
ut , 1
g 1 g var CNI
var var 1
As a result, one can show that the correlation between normal and abnormal accruals in the
absence of deviation in accounting policy and fundamentals is as follows:
*, *
corr NDAC DACC
u, t u, t1 u, t1
cov aCNI dCNI , mCNI
u, t u, t1 u, t1
var aCNI dCNI var mCNI
u, t u, t1 u, t1 u, t1
a m cov CNI , CNI d m cov CNI , CNI
2 u, t 2 u, t1 u, t u, t12ut
, 1
avarCNIdvarCNI2adcov CNI , CNI
m var CNI
2 2 2
a m g 1gdmg1g 2 2 2 2 2 2 2 2
2
agdg1g2adg1gmg1g
1 1
2
2
2
2 2
a m g g d m g g
1 2 1 1
2 2 2 4
a d g a d g m g g
1 1
1 1
m g a d g
m g a d
g
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