Transcript 슬라이드 1 - Korea University

Comparison of the Time Series Models for Trend
Analysis of Cyber Shopping Mall in South Korea
JongHoo Choi, SeungMan Hong, JongChul Shin, SunKyoung Kim, HyokMin Kwon
Department of Information and Statistics,
Korea University
Contents
1. Introduction
2. Outline of the cyber shopping mall survey
3. Data and time plot
4. Comparison of time series models
5. Discussion & Conclusions
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
Contents
1. Introduction
2. Outline of the cyber shopping mall survey
3. Data and time plot
4. Comparison of time series models
5. Discussion & Conclusions
2. Cyber Shopping Mall Survey
Cyber Shopping Mall Survey
 Monthly surveys that are performed from KNSO
(Korea National Statistical Office)
Purpose
 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
Coverage
 Internet cyber malls focused on B2C
Period
 1st ~ 22nd of every month
2. Cyber Shopping Mall Survey
Survey Items
 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
Contents
1. Introduction
2. Outline of the cyber shopping mall survey
3. Data and time plot
4. Comparison of time series models
5. Discussion & Conclusions
3. Data and time plot
Table 1. Data
year
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
month
From KNSO
3. Data and time plot
Figure 1.Time Plot
Contents
1. Introduction
2. Outline of the cyber shopping mall survey
3. Data and time plot
4. Comparison of time series models
5. Discussion & Conclusions
4. Comparison of time series models
Comparison of
time series models
1
ARIMA Model
2
Exponential Smoothing
3
Time Series Regression
ARIMA
4. Comparison of time series models

ARIMA
(AutoRegressive Integrated Moving Average)
 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)
ARIMA
4. Comparison of time series models
Figure 2. Correlogram
ARIMA
4. Comparison of time series models
Table 2. ARIMA(p,d,q) candidates
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
 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
ARIMA
4. Comparison of time series models
Figure 3. Result from ARIMA(2,1,4)
4. Comparison of time series models
Exponential Smoothing

Exponential Smoothing
 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
Exponential Smoothing
4. Comparison of time series models
Figure 4. Result from Exponential Smoothing
4. Comparison of time series models

Time Series Regression
 We applied the time series regression model as
 t sin(
zt= β0+β1t+β2t2+β3t3230
+β
4
2 cos(
t
)+β
5
30
)+εt
Time Series Regression
(Bowerman & O'Connell, 1993)
Time Series Regression
4. Comparison of time series models
Figure 5. Result from time series regression model
4. Comparison of time series models
The cross validation check is performed based on MSE criterion
Table 3. Cross validation check
Original
value
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
5478.65
337978.86
374.62
MSE
 The time series regression model seems to be the best one
4. Comparison of time series models
Figure 6. Forecasting performance
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
Contents
1. Introduction
2. Outline of the cyber shopping mall survey
3. Data and time plot
4. Comparison of time series models
5. Discussion & Conclusions
5. Discussions & Conclusions
Discussion
&Conclusions
1. Time series regression model is recommended for
forecasting of number of Cyber shopping mall
2. The data is not enough to conclude definitely
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
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