JongHoo Choi, SeungMan Hong, JongChul Shin, SunKyoung Kim, HyokMin Kwon Department of Information and Statistics, Korea University Comparison of the Time Series Models for Trend Analysis of Cyber Shopping Mall in South Korea

Contents 5. Discussion & Conclusions 4. Comparison of time series models 3. Data and time plot 2. Outline of the cyber shopping mall survey 1. Introduction

The aim of this work is to compare three time series model for trend analysis of cyber shopping mall in South Korea and perform cross validation check ARIMA Model Exponential Smoothing Time Series Regression

5. Discussion & Conclusions 4. Comparison of time series models 3. Data and time plot 1. Introduction 2. Outline of the cyber shopping mall survey Contents

Cyber Shopping Mall Survey  Monthly surveys that are performed from KNSO (Korea National Statistical Office)  Collecting detailed data to measure the size, growth and nature of E-commerce in South Korea  Serve as a useful reference for the policy-making, business management and research activities 2. Cyber Shopping Mall Survey Purpose

 Internet cyber malls focused on B2C  1st ~ 22nd of every month Period Coverage 2. Cyber Shopping Mall Survey

 8 items on general information name of the shopping mall, name of the operator company, URL, type of organization, launching date, workers, how to operate the Web site, classification of hopping mall  8 items on intensity and infrastructure of E-commerce Transaction value by category of products, size of income, composition of delivery means, composition of buyers, composition of products by type of procurement, composition of payment means, security system, authentication authority Survey Items 2. Cyber Shopping Mall Survey

5. Discussion & Conclusions 4. Comparison of time series models 2. Outline of the cyber shopping mall survey 3. Data and time plot 1. Introduction Contents

3. Data and time plot year month ,8652,2122,9963,3893,5084,3714,529 21,8672,2763,0823,4153,5254,389 31,9152,3343,1883,3963,5724,403 41,9512,3653,2423,4113,6274,421 51,9792,3723,2893,4593,7684,454 61,9982,4273,3203,4743,8564,472 72,0262,4913,3393,4744,0054,478 82,0322,5783,3433,4374,0514,490 92,0722,6573,3503,4394,1584, ,1052,7693,3533,4614,2294, ,1352,8743,3523,4784,3224, ,1682,8963,3583,4894,3554,531 From KNSO Table 1. Data HoldoutSample(test set)

Figure 1. Time Plot 3. Data and time plot

5. Discussion & Conclusions 3. Data and time plot 2. Outline of the cyber shopping mall survey 4. Comparison of time series models 1. Introduction Contents

4. Comparison of time series models Comparison of time series models Comparison of time series models 2 Exponential Smoothing Time Series Regression 3 1 ARIMA Model

 ARIMA is the best model that analysis all possible univariate time series model depend on probability process model (Box & Jenkines,1970)  We determine whether the time series we wish to forecast is stationary. If it is not, we must transform the time series using the difference  To check stationallity, we attempt to unit root test using ADF(Augmented Dickey-Fuller) statistic (Dickey&Fuller,1981) 4. Comparison of time series models  ARIMA (AutoRegressive Integrated Moving Average) ARIMA

4. Comparison of time series models Figure 2. Correlogram ARIMA

AICSBCSEAICSBCSE ARIMA(2,1,4) ARIMA(2,1,1) ARIMA(4,1,2) ARIMA(4,1,1) ARIMA(4,1,3) ARIMA(2,1,2) ARIMA(3,1,1) ARIMA(3,1,2) ARIMA(1,1,4) ARIMA(1,1,2) Table 2. ARIMA(p,d,q) candidates  We select the best 10 models among the all possible combination based on the model selection criteria of AIC, SBC and SE  ARIMA(2,1,4) is recommended for the analysis 4. Comparison of time series models ARIMA

Figure 3. Result from ARIMA(2,1,4) 4. Comparison of time series models ARIMA

 Smoothing Constant value is from One-Parameter Double Exponential Smoothing  In most exponential smoothing applications, the value of the smoothing constant used is between 0.01 and 0.30 (Bowerman & O'Connell, 1993)  As it is less than 0.3, One-Parameter Double Exponential smoothing is recommended 4. Comparison of time series models  Exponential Smoothing Exponential Smoothing

Figure 4. Result from Exponential Smoothing 4. Comparison of time series models Exponential Smoothing

4. Comparison of time series models  Time Series Regression  We applied the time series regression model as z t = β 0 +β 1 t+β 2 t 2 +β 3 t 3 +β 4 sin( )+β 5 cos( )+ε t (Bowerman & O'Connell, 1993) Time Series Regression

Figure 5. Result from time series regression model 4. Comparison of time series models Time Series Regression

Original value ARIMA Expected Exponential Smoothing Time Series Regression Jul Aug Sep Oct Nov Dec Jan MSE Table 3. Cross validation check The cross validation check is performed based on MSE criterion  The time series regression model seems to be the best one 4. Comparison of time series models

Figure 6. Forecasting performance ExponentialSmoothing ARIMA Time SeriesRegression 4. Comparison of time series models

 Time series regression models is the best one for long-term forecasting  It is relevant to the result of cross validation check 4. Comparison of time series models

3. Data and time plot 2. Outline of the cyber shopping mall survey 5. Discussion & Conclusions 1. Introduction Contents

The further research - Trend analysis of the sales amount of cyber shopping mall - Compare general malls with specialized malls - Investigate into the co-movement of the economic time series with cyber shopping trend Discussion &Conclusions Discussion &Conclusions 2. The data is not enough to conclude definitely 1.Time series regression model is recommended for forecasting of number of Cyber shopping mall 5. Discussions & Conclusions

References Akaike, H. (1976). Canonical Correlations Analysis of Time Series and the Use of an Information Criterion. System Identification: Advances and Case studies (Eds.R.Mehra and D.G.Lainiotis), 27-96, New York : Academic Press. Box, G. E. P. and Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control, San Francisco : Holden-Day. Bowerman, B. L. and O'Connell, R. T. (1993). Forecasting and Time Series : An Applied Approach, 3rd Edition, California : Duxbury Press. KNSO(2006) Schwarz, G. (1978). Estimating the Dimension of a Model, The Annals of Statistics, Vol. 6, No.2,

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