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CPS2134 Yutaka Kuroki et al.
            Generalized  Method  of  Moment  (GMM).  GMM  has  become  an  important
            estimation procedure in applied economics and finance since Hansen (1982)
            introduce.  Finally,  we  confirm  the  validity  of  our  model  and  proposed
            fundamental factors in retail demand series.
                The rest of paper is organized as follows. Section 2 describes data and our
            proposed model. The proposed fundamental factors in restaurant visitor data
            are also introduced in Section 2. Section 3 shows estimation results of the
            multiple regression models together with the results of the tests of the model
            assumptions. Section 4 provides summary and discussions of our results.

            2.  Data and Fundamental Factors in Retail Demand
                The number of customers for Japanese restaurants were recorded by using
            AirREGI systems of Recruit Holdings, where AirREGI provides a free POS cash-
            register service. The data were available from Kaggle Recruit restaurant visitor
                                     1
            forecasting  competitions .  The  data  consists  of  number  of  visitors  for  795
                                                                     nd
                                                 st
            restaurants in Japan from the period 1   January 2016 to 22   April 2017. Area
            covered all major cities in Japan, including Sapporo, Tokyo, Osaka, Fukuoka,
            and  so  on.  The  genres  or  styles  of  the  restaurants  are  divided  into  14
            categories, e.g., Japanese food, Italian/French, and Café/Sweets, and so on.
            Figure 1 shows the mean number of daily customers of whole restaurants in
            the observed period. Seasonal fluctuations along with large gaps around the
            year end and beginning are apparent.  The time-series structures of the mean
            number of the customers are highly correlated and annual trend with weekly
            seasonal patterns is also observed. The data includes the records for closed
            days, which are indicated by 0 records. The patterns of the frequency of 0
            records are random and depends on situations for each restaurant. In this
            study,  we  propose  the  factor  models  for  the  prediction  of  the  number  of
            customers on each restaurant, we need to pay attention for 0 records of the
            data.
















                Figure 1. Time series plots for the mean number of daily customers of whole
                                             restaurants


            1  https://www.kaggle.com/c/recruit-restaurant-visitor-forecasting
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