Sustainable Development in Popular Newspapers: How is coverage in De Telegraaf influenced by other newspapers’ attention to sustainable development? ARIMA modelling with (G)ARCH and Fractional Integration

1. Sustainable Development in Popular Newspapers
How is coverage in De Telegraaf influenced by other
newspapers’ attention to sustainable development?
ARIMA modelling with (G)ARCH and Fractional Integration
Assignment 6
Mark Boukes (markboukes@Hotmail.com)
5616298
1st semester 2010/2011
Dynamic Data Analysis
Lecturer: Dr. R. Vliegenthart
December 23, 2010
Communication Science (Research MSc)
Faculty of Social and Behavioural Sciences
University of Amsterdam

3. Table of contents
INTRODUCTION.............................................................................................................................................1
METHOD........................................................................................................................................................1
RESULTS........................................................................................................................................................2
ARIMA MODEL.......................................................................................................................................................2
THE CONDITIONAL VARIANCE..........................................................................................................................................5
CONCLUSION.................................................................................................................................................6
REFERENCE....................................................................................................................................................6
DO FILE..........................................................................................................................................................6

5. Introduction
In this study I aim to investigate the influence news coverage in a particular newspaper has on
the coverage of another newspaper. For this purpose, I have chosen a specific topic,
sustainable development, that seems to get a lot media attention in the last years. The topic of
sustainable development was chosen, because it can be related to several parts of society, such
as the economy, science and also for the man in the street this topic is relevant.
As those different parts of society are represented by different media, it is interesting
to see how they influence each other on the amount of attention that is paid to this issue. Will
an increase in attention of business men’s newspapers result in an increase of attention in
newspapers that deal with popular issues; and how is this newspaper affected by a newspaper
that is more focused on scientific issues? In brief, How is the attention in a popular
newspaper caused by attention in scientific and economic newspapers. The most read popular
newspaper in the Netherlands is De Telegraaf, a newspaper that has a main financial or
business focus is Het Financieele Dagblad, and NRC Handelsblad is known for its relative
large attention to scientific developments. The effects of both Het Financieele Dagblad and
NRC Handelsblad are expected to be positive on the coverage of De Telegraaf. My hypothesis
is therefore:
An increase in the number of articles about sustainable development in Het Financieele
Dagblad or in NRC Handelsblad is likely to be followed by a increase in the number of
articles this topic in coverage of de Telegraaf in future weeks.
Method
In order to investigate whether changes in the number of articles about sustainable development
in NRC Handelsblad and Het Financieele Dagblad have an effect on De Telegraafs’s news, a
dataset was created via a computer-assisted content analysis, which was conducted using the
digital archive of the Web-based version of LexisNexis. Articles were selected via the
Boolean search term duurza! OR "groene energie" OR "zonne-energie" OR "windenergie".
The period I analyzed was from 1 January 1999 until 31 December 2009. This period was
chosen, because information about De Telegraaf is only available from 1999. The search
procedure was repeated three times; one time for every newspaper, so three variables could be
created by aggregating the data on a weekly basis. A weekly basis is chosen, because it is
more detailed than the monthly basis, whereas a daily basis would lead to many days on
which no coverage was found, what consequently meant that a lot cases had to be filled in by
hand. A total of 35225 articles were found for 581 weeks; 18501 in Het Financieele Dagblad,
10335 in NRC Handelsblad and 6389 in De Telegraaf.
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6. To analyse the effects on the coverage of De Telegraaf, first an adequate ARIMA
model is developed using Stata 10.1 for the time series of this variable, this was followed by
adding a GARCH term to model the volatility, thereafter the independent variables were
added to the model, resulting in a multivariate ARIMA model.
Results
In this results section, I specify how the analysis was conducted and discuss the results that
were found. I followed the ARIMA-framework described by Vliegenthart (n.d.) to make the
base ARIMA-model, thereafter GARCH-terms were added to take heteroscedasticity into
account and finally the independent variables were added to the model.
ARIMA model
Figure 1 plots the time series of the attention in the three newspapers for the period that we
are studying. It seems that Het Financieele Dagblad pays the most attention to sustainable
development and De Telegraaf the least attention. The amount of attention seems to be rising
a little over time, but this is not confirmed by augmented Dickey-Fuller tests (see Table 1);
hypotheses for unit root are rejected. However the results were close to insignificant and the
graphs also show that there is some upward trend. Therefore, the data were fractionally
integrated at a level of 0.352 following the Robinson (1995) multivariate estimate of the long
memory (fractional integration) parameters for the number of articles in De Telegraaf.
Figure 1. The number of articles about sustainable development over time in the three
newspapers of interest.
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7. Table 1. The results of augmented Dickey-Fuller tests for the amount of articles over time
Augmented Dickey-Fuller test Telegraaf FD NRC
Random walk without drift -6.560 -4.990 -5.596
Random walk with drift -10.878 -10.104 -14.525
Random walk with drift and trend -16.487 -15.716 -16.751
FI.Telegraaf FI.FD FI.NRC
Random walk without drift -11.756 -8.938 -10.011
Random walk with drift -18.478 -17.020 -22.947
Random walk with drift and trend -25.563 -24.102 -25.383
Note. All tests indicate the absence of a unit root. FI, fractionally integrated
The next step was predicting the number of articles about sustainable development as good as
possible by accounting for its own past, either with autoregressive (AR) terms, moving
average (MA) terms or both. This was done by inspecting the autocorrelation (ACF) and
partial autocorrelation functions (PACF). The ACF graph showed an unclear pattern, while
the PACF graph displays a declining pattern for the first lags. This pattern is indicative for a
process with a moving average at lag 1. A ARIMA (0,0.352,1) model seems thus the right
choice. This model was tested for autocorrelation with the Ljung–Box Q test statistic and for
the presence of conditional heteroscedasticity with the Engle-Granger test. A significant result
for the Ljung-Box Q-test for autocorrelation (20 lags) was found, meaning that the null
hypothesis of white noise was rejected and that the absence of autocorrelation cannot be
assumed (Q = 807.40, p < 0.001). Therefore, to avoid autocorrelation in the ARIMA-model, it
was extended with an autoregressive term at lag 1 and a moving average term at lag 2;
following the ACF and PACF graphs for every extension until the residuals of the AR(1)-
I(0.352)-MA(1,2)-model did reflect no autocorrelation (Q = 24.89, p = 0.206). However, it
seems not possible to reduce the Ljung-Box test statistic Q2 based on the squared residuals to
insignificance, with AR or MA terms only. This means that there is a strong temporal
dependency in the variance of the number of Telegraaf articles about sustainable
development; heteroscedasticity. Residuals of the last ARIMA model were saved and are later
analysed to see how the conditional variance of the number of articles in De Telegraaf was
affected by changes in the number of articles in the other two newspapers.
To avoid the heteroscedasticity in the model, it was necessary to model also the
conditional variance of the dependent variable, either with autoregressive conditional
heteroscedasticity (ARCH) terms or with a combination of ARCH and generalized
autoregressive conditional heteroscedasticity (GARCH) terms. This last option was chosen,
because it has considerable better model fit according to Akaike Info Criterion (AIC) and the
3

8. Bayesian information criterion (BIC) (ΔAIC = 104.94, ΔBIC = 100.573). The results of this
general model are showed in Table 2. The ARCH and GARCH terms are both statistically
significant and positive. This indicates that that innovations in the prior period increase
conditional variance in a next period. Periods of high volatility are thus likely to be grouped
together in time. The autoregressive and moving average terms are also significant, meaning
that a particular number of articles in some week in De Telegraaf, are partly determined by
the number of articles in this newpaper the week before and two weeks before.
Table 2. GARCH models: number of Telegraaf articles about sustainable development
General GARCH model GARCH with independent variables
Constant 2.502 (0.634)* 1.637 (0.638)*
Autoregressive (t - 1) 1.007 (0.001)* 1.007 (0.001)*
Moving average (t - 1) -1.125 (0.045)* -1.154 (0.046)*
Moving average (t - 2) 0.128 (0.045)* 0.156 (0.046)*
ARCH term 0.050 (0.013)* 0.047 (0.012)*
GARCH term 0.958 (0.010)* 0.961 (0.010)*
NRC Handelsblad (t - 1) 0.052 (0.030)a
Het Financieele Dagblad (t - 1) 0.047 (0.023)*
Ljung-Box Q(20) residuals 25.92 25.91
AIC 3599.80 3590.38
BIC 3630.34 3629.63
Note. Unstandardized coefficients. Standard errors in parentheses;
* p < 0.05 , a = 0.091
Now a model was built that properly accounts for its own past and heteroscedasticity, the
analysis could go on with the next step: assessing the impact of the amount of news coverage
about sustainable development in NRC Handelsblad and Het Financieele Dagblad on that of
the coverage in De Telegraaf. The cross-correlation function (CCF) for the residuals of this
GARCH model and for the amount of coverage in NRC, and the CCF for the residuals with
the coverage in Het Financieele Dagblad, indicate both that strong association is present when
coverage in both newspapers is lagged at 1 week. The results of the GARCH model that
included these two independent variables can also be found in Table 2.
The results indicate that news coverage about sustainable development in Het
Financieele Dagblad (FD) had a significant positive effect on coverage about this issue in De
Telegraaf. A one article increase in FD, did on average result in a 0.05 article increase in the
next week’s coverage of De Telegraaf. The effect of NRC Handelsblad is not significant,
following a two-tailed test with 95% confidence interval. However, because this effect is
expected to be positive, a one-tailed test can be used. Then the effect of NRC Handelsblad’s
4

9. coverage about sustainable development also becomes significant (χ2 = 2.85, p = 0.0456). A
one article increase about sustainable development in NRC Handelsblad, will on average also
result in a 0.05 article increase in De Telegraaf. Both effects seem thus to be rather weak.
The conditional variance
As written before, the ARIMA-model was highly volatile, meaning that the variance was not
stabile over time. This heteroscedasticity could not be reduced by adding more autoregressive
or moving average terms, but a GARCH model had to be used. Though this heteroscedasticity
was unpleasant in the attempt to predict the numbers of articles published by De Telegraaf
about sustainable development, it can also be used as interesting information. Consequently, I
would like to know whether the conditional variance was affected by developments in the
numbers of articles published by the other newspapers. Therefore, the squared residuals of the
AR(1)-I(0.352)-MA(1,2)-model were used as dependent variables.
The time series of this variance-variable was stationary according to augmented
Dickey-Fuller tests. Following the same framework (Vliegenthart, n.d.) as was done above, a
ARIMA(1,0,1)-model was built that did neither reflected autocorrelation (Q = 28.90, p =
0.09), nor heteroscedasticity (Q = 1.29, p = 0.999) in the residuals of the predictions of the
variance of the fractionally integrated number of articles in De Telegraaf. The next step was
to insert the same independent variables as in the GARCH model, because the cross-
correlation function indicates that the residuals of this model correlate most strongly with the
fractionally integrated values of the other two dependent variables at a lag of one week. The
results of this model can be found in Table 3.
Table 3. ARIMA model for the variance of the fractionally integrated number of articles in De Telegraaf
ARIMA (1,0,1)
Constant 3.740 (0.681)
Autoregressive (t - 1) -0.737 (0.857)
Moving average (t - 1) 0.708 (0.944)
NRC Handelsblad (t - 1) 0.502 (1.404)
Het Financieele Dagblad (t - 1) 1.413 (0.681)*
Ljung-Box Q(20) residuals 28.79
Ljung-Box Q(20) residuals2 1.97
AIC 7149.06
BIC 7175.23
Note. Unstandardized coefficients. Standard errors in parentheses;
* p < 0.05
News coverage about sustainable development in NRC Handelsblad does not influence the
variance of the fractionally integrated number of articles in De Telegraaf. Interestingly, this
5

10. variance was significantly and positively affected by news coverage in Het Financieele
Dagblad. This means that when the fractionally integrated number of articles about
sustainable development in Het Financieele Dagblad increased, the variance in the number of
articles in De Telegraaf also increased and it thus became more difficult to predict this values
precisely. The results of the ARIMA-model make clear that the variance on a certain moment
is not strongly affected by previous variance, as both the AR and the MA-term are
insignificant.
Conclusion
This study has found that changes in the number of articles about sustainable development in
the scientifically oriented newspaper NRC Handelsblad and the business oriented newspaper
Het Financieele Dagblad, both lead to changes in the same direction in the number of articles
about this topic in the popular newspaper De Telegraaf. A GARCH-model was used to
analyse this data, as the dependent variable had a volatility that was high at certain moments.
Because this heteroscedasticity was an interesting part of the dependent variable
another model was developed to predict volatility. The ARIMA-model that was built for this
purpose, found that variance could partly be predicted by the fractionally integrated number
of articles about sustainable development in Het Financieele Dagblad, but not by the coverage
of NRC Handelsblad.
Reference
Robinson, P. M. (1995). Log-periodogram regression of time series with long range
dependence. Annals of Statistics, 23(3), 1048-1072.
Vliegenthart, R. (n.d.). Moving up. Applying aggregate level time series analysis in
communication science. Unpublished manuscript.
Do File
tsset week, weekly
twoway (tsline FD, lcolor(red)) (tsline NRC, lcolor(green) lpattern(dash)
lwidth(medthick)) (tsline Telegraaf, lcolor(blue) lpattern(dash)
lwidth(medium))
twoway (tsline FD, lcolor(red))
*with drift
dfuller Telegraaf
*random walk
dfuller Telegraaf, noconstant
*trend
dfuller Telegraaf, trend
*with drift
dfuller FD
*random walk
dfuller FD, noconstant
6

11. *trend
dfuller FD, trend
*with drift
dfuller NRC
*random walk
dfuller NRC, noconstant
*trend
dfuller NRC, trend
search ARFIMA
roblpr Telegraaf
gen dfTelegraaf=Telegraaf-.3520017*l.Telegraaf
gen dfNRC=NRC-.3520017*l.NRC
gen dfFD=FD-.3520017*l.FD
*with drift
dfuller dfTelegraaf
*random walk
dfuller dfTelegraaf, noconstant
*trend
dfuller dfTelegraaf, trend
*with drift
dfuller dfFD
*random walk
dfuller dfFD, noconstant
*trend
dfuller dfFD, trend
*with drift
dfuller dfNRC
*random walk
dfuller dfNRC, noconstant
*trend
dfuller dfNRC, trend
ac dfTelegraaf
pac dfTelegraaf
corrgram dfTelegraaf
*The ACF graph shows a clear spike a unclear pattern, while the PACF graph
displays a declining pattern for the first lags.
*A ARIMA (0,fi,1) model seems thus the right choice
arima dfTelegraaf, ma(1)
estat ic
predict r, res
gen r_s= r*r
wntestq r, lags(20)
wntestq r_s, lags(20)
ac r
pac r
drop r r_s
*Q(r) and Q(r2) significicant, a peak at lag 2
arima dfTelegraaf, ma(1 2)
estat ic
predict r, res
gen r_s= r*r
wntestq r, lags(20)
7

12. wntestq r_s, lags(20)
ac r
pac r
drop r r_s
arima dfTelegraaf, ar(1) ma(1 2)
estat ic
predict r, res
gen r_s= r*r
wntestq r, lags(20)
wntestq r_s, lags(20)
ac r
pac r
drop r r_s
*Q(r) insignificant but Q(r2) significicant
arch dfTelegraaf, ar(1) ma(1 2) arch(1)
estat ic
arch dfTelegraaf, ar(1) ma(1 2) arch(1) garch(1)
estat ic
di 3704.739 - 3599.802
di 3730.917 - 3630.344
predict r, res
gen r_s= r*r
wntestq r, lags(20)
wntestq r_s, lags(20)
ac r
pac r
drop r r_s
*Q(r) stays insignificant. Now the model is ok!
*now see how the residuals of this models are best predicted by which lags
for NRC and FD
arch dfTelegraaf, ar(1) ma(1 2) arch(1) garch(1)
estat ic
predict r, res
xcorr r dfNRC, lags(13)
xcorr r dfFD, lags(13)
*both strongly correlate at the first lag
drop r
arch dfTelegraaf l1.dfNRC l1.dfFD, ar(1) ma(1 2) arch(1) garch(1)
estat ic
predict r, res
gen r_s= r*r
wntestq r, lags(20)
wntestq r_s, lags(20)
drop r r_s
test l1.dfNRC
di 0.0912/2
*****Explaining conditional variance****
*final arima model
arima dfTelegraaf, ar(1) ma(1 2)
predict r, res
gen sArima=r*r
drop r
twoway (tsline sArima, lcolor(black))
8

13. *with drift
dfuller sArima
*random walk
dfuller sArima, noconstant
*trend
dfuller sArima, trend
ac sArima
pac sArima
corrgram sArima
arima sArima
estat ic
predict r, res
gen r_s= r*r
wntestq r, lags(20)
wntestq r_s, lags(20)
ac r
pac r
drop r r_s
arima sArima, ar(1) ma(1)
estat ic
predict r, res
gen r_s= r*r
wntestq r, lags(20)
wntestq r_s, lags(20)
drop r r_s
arima sArima, ar(1) ma(1)
predict r, res
xcorr r dfNRC, lags(13)
xcorr r dfFD, lags(13)
arima sArima l1.dfNRC l1.dfFD, ar(1) ma(1)
estat ic
predict r, res
gen r_s= r*r
wntestq r, lags(20)
wntestq r_s, lags(20)
drop r r_s
9