2012. Vol.3, No.8, 610-612
Published Online August 2012 in SciRes (
Copyright © 2012 SciRes.
Volatility Analysis of Web News and Public Attitude
by GARCH Model
Pinrui Yu1, Tianzhen Liu2, Qian Ding2*
1School of Journalism and Communication, Southwest University, Chongqing, China
2School of Urban Design, Wuhan University, Wuhan, China
Email: *
Received May 7th, 2012; revised June 2nd, 2012; accepted July 5th, 2012
GARCH (Generalized Auto-Regressive Conditional Heteroskedasticity) model proposed by Professor
Engle is successful to analyze the volatility of stock price. In this paper GARCH model is used to analyze
the volatility of web news events and public attitudes by the data coming from typical news events in fa-
mous web. The results show that the volatility of web news events and public attitudes are suitable to
GARCH model by some adjusting and test of parameters.
Keywords: Web News; Public Attitude; Volatility Analysis; GARCH Model
Social hot news spread rapidly in internet with abundant in-
formation. The news may cause psychological reactions of public
with some attitudes or moods: delight, moved, sympathy, angry,
funny, sad, novel, sweat, and so on as Figure 1. The summaries
of these attitudes are also called as “public attitudes”. To reveal
the relationship between public events and public attitudes or
opinions, it is necessary to make quantitative analysis, espe-
cially volatility analysis by webometrics (Tomas et al., 1997).
There are some quantitative researches on public attitudes of
social hot news in website. Researchers get the data from web
forums and news website, and analyze the evolvement of public
attitudes in these news examples by statistical modeling. Xie
(2006) proposed ten analysis modes such as hot sports, empha-
sis, focus, sensitive points, frequency points, etc. Wei (2006)
divided evolvement modes of crisis events into four categories
by statistical distributions: exponential type, normal type,
Poisson type, fluctuation type. Qi (2008) proposed an evalua-
tion method of public attitudes by ARMA model and regression
model. Lu (2010) explored the rule of spread of public attitude
by variation number, correlation analysis, Tobit model. Sun
(2011) built monitor and analysis model of spread of public
attitude in web by agent. In fact, attitude problems in web be-
long to psychological problems which have been studied using
mathematical models successfully (Tong, 2010; Lin, 2011).
The public attitudes occurred by emergencies have volatil-
ities with irregular variance similar to the prices of many stocks.
Professor Engle (1982) proposed Auto-Regressive Conditional
Heteroskedasticity (ARCH) model to analyze the volatility of
stock price successfully and obtained Nobel Prize in Economics
in 2003. His student Bollerslev (1996) proposed Generalized
ARCH (GARCH) model and developed the thought of Engle.
Almost there is not any paper to use GARCH model to analyze
the volatility of public attitudes occurred by web news. So we
probe the method using GARCH model to analyze the volatility
of public attitudes occurred by web news.
The Volatility Characters of Public
Attitudes in Web
In general, an evolvement process of public attitudes in web
has three stages: initial stage, rapid spread stage, and subsiding
stage, similar to the process of the life of a man [11]. Figure 1
shows the three stages of post amount about “Wu-Kan event” in
the “Baidu Web” (Figure 2). In the initial stage, the post
amount is small and can not distinguish from common case
easily. In the second stage, the post amount increase rapidly,
and if we guide the opinions in time we can control the events
correctly. We notice that the subsiding process is not smooth
but may have some small waves in this stage.
Figure 1.
Survey figure for mood of news events in Tencent Web.
Figure 2.
*Corresponding author. Three stages of post amount about “Wu-Kan event”.
The post amount of news events in web is a time series, and
has some characters as follows.
1) Clustering. This means the volatility of post amount is not
single. A big wave is always followed many big waves, and a
small wave is always followed many small waves. These phe-
nomena show that there are herd mentalities in web hot events.
2) Sharp leptokurtic with fat tail in the density curve. We can
draw the density curve of post amount, and find it does not
appear as normal distribution, but has sharp leptokurtic with fat
tail similar to the density curve of stock prices. In general, an
emergency outbreaks suddenly and its affection dissipates
slowly, so its density curve has a single fat tail on the right.
3) Leverage effect. In the spread process of news information
in web, positive information or negative information may affect
volatility of public attitudes greatly. Especially, the negative
information may affect volatility of public attitudes more seri-
4) Long Memory. The autocorrelation function of the series
of volatility of public attitudes decreases very slowly. That is,
the autocorrelation function between two sub-series with long
distance is significant yet. This means a history event may af-
fect public attitudes for a long time.
These characters can not be explained by ARMA model or
Random Walk model, but can be explained by ARCH model
and GARCH model easily.
Suppose yt is a time series, ARCH(q) model can be expressed
as following formula:
he t
  (3)
where Xt is a explanatory variable, β is a coefficient vector, εt is
the error term with mean 0, but his variance is not constant. It is
interesting the hypothesis about εt in ARCH model is too com-
plex with (2) and (3), where E(et) = 0, D(et) = 1. To guarantee
the second-order stability of series yt, it is necessary to demand
all characteristic roots of ht = 0 must be outside the unit circle.
GARCH (p, q) model only generalizes (3) in ARCH(q)
model as (4):
011 11ttqtqtp
  
In GARCH (p, q) model, when p = 0, the model becomes
common ARCH (q) model. When q = p = 0, εt is a common
white noise, and the model becomes common linear regression
model. In general, GARCH (1, 1) or GARCH (2, 2) are suffi-
cient to fit and forecast volatilities of public attitudes. More
details about GARCH models can be found in “Developing
Econometrics”, Chapter 8, Multivariate and Nonstationary
Time Series Models (Tong et al., 2011).
Volatility Analysis of Public Attitudes by
We select the hottest social event in 2011, Wu-Kan event, as
research object to analyze its volatility of public attitudes by
GARCH model.
Wu-Kan event is a typical conflict between local government
and the people involving economic interest. In September 2011,
the leader of Wu-Kan villages sold the land to developer and
got a huge profit, but the people only obtained a few benefits.
Economic interests lead to political conflict for three months.
Serious political conflict caused attention of senior leadership.
At last, the conflict is satisfactorily resolved, and the event
subsides from line of sight of public gradually.
We collect the data from December 1, 2011 to March 31,
2012 from Baidu Web by keyword “Wu-Kan event”, and obtain
121 numbers.
We use four models, GARCH (1, 1), GARCH (1, 2),
GARCH (2, 1), GARCH (2, 2), to compare their fitting effects
by the significant of test. The selected model at last has the
minimum value of AIC and SC criterion and the maximum
value of likelihood. The results of calculation are in Table 1.
Comparing with the results in Table 1, we select model
GARCH (1, 2) as the optimal model. The parameters of
GARCH (1, 2) are calculated as follows:
0.7584 0.1334
Table 1.
The statistics of GARCH models.
GARCH (1, 1)GARCH (2, 1) GARCH (1, 2) GARCH (2, 2)
AIC–.5967 –.7025 –.6062 –.4873
SC –.5028 –.5895 –.4933 –.3557
Log52.4909 62.1998 54.2613 45.4588
R2 –.5907 .0233 .1623 .1858
Figure 3.
The fitting effect of model GARCH (1, 2).
Copyright © 2012 SciRes. 611
0.0014 0.00120.015320.8123
  2
Figure 3 shows the fitting effect of GARCH (1, 2) with the
original data, which is calculated by the software DASC (Data
Analysis & Statistical Computation, Tong, 2005).
It is important to capture the big volatility in analysis of the
public attitude in web news events. This is good for the fore-
casting and pre-waning of emergency. From Figure 3 we are
satisfied with model GARCH (1, 2).
We can see the affections of the rate of change by the new
information from the coefficients of model GARCH (1, 2).
Besides, the coefficient (.8123) reflects long memory in system.
At last, the sum of three coefficients is less than 1 which shows
the system is stable.
Advanced statistical tools in modern network provide con-
venient conditions for our access to the Internet public opinion
data. Our work shows that the volatilities of public attitudes in
web have the character of heteroskedasticity, so it is suitable to
use GARCH model. Further more, adjusting and test parame-
ters of model is important to obtain good fitting effect, and the
fitting figure is good tool to distinguish the effect of the model.
The work of this paper is only to focus on the basic data of
public attitude. More deep research should focus on sensibility
analysis by text information, which is more complex and inter-
The authors thank Professor Tong Hengqing for his guidance.
The project was supported by the National Natural Science
Foundation of China (60773210).
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