JongHoo Choi, SeungMan Hong, JongChul Shin, SunKyoung Kim, HyokMin KwonDepartment of Information and Statistics, Korea University

Comparison of the Time Series Models for Comparison of the Time Series Models for Trend Analysis of Cyber Shopping Mall in Trend Analysis of Cyber Shopping Mall in South KoreaSouth 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

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

yearmonth 2001 2002 2003 2004 2005 2006 2007

1 1,865 2,212 2,996 3,389 3,508 4,371 4,529

2 1,867 2,276 3,082 3,415 3,525 4,389

3 1,915 2,334 3,188 3,396 3,572 4,403

4 1,951 2,365 3,242 3,411 3,627 4,421

5 1,979 2,372 3,289 3,459 3,768 4,454

6 1,998 2,427 3,320 3,474 3,856 4,472

7 2,026 2,491 3,339 3,474 4,005 4,478

8 2,032 2,578 3,343 3,437 4,051 4,490

9 2,072 2,657 3,350 3,439 4,158 4,504

10 2,105 2,769 3,353 3,461 4,229 4,518

11 2,135 2,874 3,352 3,478 4,322 4,524

12 2,168 2,896 3,358 3,489 4,355 4,531

From KNSO

Table 1. Data

Holdout

Sample

(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

22 Exponential Smoothing

Time Series Regression

33

11 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)

4. Comparison of time series models

Figure 2. Correlogram

AIC SBC SE AIC SBC SE

ARIMA(2,1,4) 618.11 633.99 26.84 ARIMA(2,1,1) 623.39 632.09 28.40

ARIMA(4,1,2) 618.26 631.31 26.92 ARIMA(4,1,1) 625.42 636.29 28.64

ARIMA(4,1,3) 619.20 632.24 27.12 ARIMA(2,1,2) 625.51 635.21 29.09

ARIMA(3,1,1) 620.59 629.29 27.80 ARIMA(3,1,2) 626.94 635.63 29.19

ARIMA(1,1,4) 621.81 630.51 28.06 ARIMA(1,1,2) 627.98 636.68 29.42

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

Figure 3. Result from ARIMA(2,1,4)

4. Comparison of time series models

Smoothing Constant value is 0.105

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

Figure 4. Result from Exponential Smoothing

4. Comparison of time series models

4. Comparison of time series models

Time Series Regression

We applied the time series regression model as

zt= β0+β1t+β2t2+β3t3+β4sin( )+β5cos( )+εt

(Bowerman & O'Connell, 1993)

230t 2

30t

Figure 5. Result from time series regression model

4. Comparison of time series models

Originalvalue

ARIMA Expected

Exponential Smoothing

Time Series Regression

Jul.2006 4478 4500.36 4548.23 4481.88

Aug.2006 4490 4514.42 4592.32 4490.65

Sep.2006 4504 4543.87 4636.41 4499.78

Oct.2006 4518 4575.97 4680.49 4511.16

Nov.2006 4524 4601.65 4724.58 4526.61

Dec.2006 4531 4626.12 4768.67 4547.85

Jan.2007 4529 4660.24 4812.76 4576.44

MSE 5478.65 337978.86 374.62

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

Exponential

Smoothing

ARIMA

Time Series

Regression

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

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 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&ConclusionsDiscussion&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) http://kosis.nso.go.kr/cgi-bin/sws_999.cgi?ID=DT_1KE1001&IDTYPE=3

Schwarz, G. (1978). Estimating the Dimension of a Model, The Annals of Statistics, Vol. 6, No.2,461-464.

Q & A