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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