Page 102 - Contributed Paper Session (CPS) - Volume 4

CPS2134 Yutaka Kuroki et al.
Let Y denote the number of customers for the -th restaurant at time .

The first step for data screening is to impute 0 records with time series forecast
of the following regression model:
if ≠ 0,
,
,
̃
= {
,
̂
if = 0,
,
,
where
7
̃
̂
̂

= + ∑ ̂ , , + .
,
,
,

=1
Where is m-dimensional factor vector explained later, , is dummy
variable for each day of week, is a dummy variable for holidays and

, , , are the OLS estimates of the regression coefficients.
,
,

Using these complete panel data , the following multiple factor models
are defined as follows,
7
− ̅

, = ∑ , , + + ∑ + , , = , .
,
,
, ,
2
=1 =1 √ ( − ̅̅̅̅)
, ,

The fundamental retail demand factors we use in this study is Market (MKT),
Small minus Big (SMB), and Safe minus Risky (SMR) factors. Similar to the
factor models used for asset returns modeling, we estimated SMB and SMR
by calculating the difference of returns between two portfolios based on
corresponding features of restaurants. To construct big restaurants portfolio
and small restaurants portfolio, we used mean customer counts for each
restaurant and classified each restaurant into “big” and “small” categories.
Then the SMB (Small minus Big) factor can be obtained by subtracting these
normalized small and big portfolios. Similarly, SMR (Safe minus Risky) factor
can be obtained as follows. We calculate the coefficient of variation for each
( , )
store, that is = , then we classified each restaurant into “Safe” and

( , )
st
rd
“Risky ”categories, whose falls into 1 and 3 quantiles of the samples,

respectively. The MKT factor is estimated by removing seasonality from
,
with SARIMA model, since MKT factor should be constructed to be
uncorrelated with seasonal patterns of the observed series.
Figure 3 shows constructed three factors. According to these plots, we can
see that the MKT factors have no apparent seasonal patterns whereas this
factor explains some sort of overall trend of the number of customers. The
SMB factor becomes large around the year end, which indicates the large
profitable opportunities increases for larger stores. On the other hand, the
SMR factor becomes small around year end, which indicates that stores have

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