Page 105 - Special Topic Session (STS) - Volume 4

STS566 K. Prokopenko et al.
The normalization procedure was applied to deliver more stationary data sets.
It should be noted that normalized payments have quite more stable behavior
than original ones (Fig. 7).

Fig. 7. Stationarity check of 670 branches using Fisher criteria (F-test). Values from each
branch were divided by their weekly total value and tested using Fisher criteria for alpha =
0.01, N = 592, V = 1.21. Number of branches with stationary incoming payments: 428
(63.88%), stationary outgoing payments: 408 (60.90%).

3. Complex Seasonal ARMA model of cash payments
During research provided the following assumptions were stated, proved
and then accepted as root points of the forecasting approach:
1. Weekly aggregated cash payments as time series has strict general
trend and annual seasonality. For weekly aggregated series it usually
has 52 full weeks seasonality.
2. Each branch has strict weekly coefficient shape. For example, for
specific branch Monday’s incoming payments can usually have 40% of
total weekly incoming payments.
3. Coefficients of week days can also have seasonality behavior.
4. Payments normalization is a way to make data sets more stationary.

According to statements above cash payments model
, , … , , , , … , ,
1
1

( ) , = 1, . . . ,7 can be expressed as a

, , … , , , , … , , ,

1
1
recursive multi-layer seasonal autoregressive model of daily cash payments
:

7+1
= 7+1 ∗ 7+1 + (1)

Where is daily cash payment value at current date with index , 7+1 is

7+1
total payment of week where current date is placed, 7+1 is coefficient of
week day of current date, is white noise.

Trend in (1) is a seasonal autoregressive process explained by:
+ , > + (, ) (2)
+ ∑
= ∑ − −−

=1
=1

where and are the order and coefficients of trend autoregressive model,

, and are the order, coefficients and lag of seasonal part of trend

autoregressive model, is white noise. Weekdays coefficients , = 1, … ,7

are also set of seasonal autoregressive processes explained by:
94 | I S I W S C 2 0 1 9