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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
 

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

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Sustainable Development in Popular Newspapers: How is coverage in De Telegraaf influenced by other newspapers’ attention to sustainable development? ...

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

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    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 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 Document Transcript

    • Sustainable Development in Popular NewspapersHow is coverage in De Telegraaf influenced by othernewspapers’ 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
    • Table of contentsINTRODUCTION.............................................................................................................................................1METHOD........................................................................................................................................................1RESULTS........................................................................................................................................................2 ARIMA MODEL.......................................................................................................................................................2 THE CONDITIONAL VARIANCE..........................................................................................................................................5CONCLUSION.................................................................................................................................................6REFERENCE....................................................................................................................................................6DO FILE..........................................................................................................................................................6
    • IntroductionIn this study I aim to investigate the influence news coverage in a particular newspaper has onthe 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 ofsustainable development was chosen, because it can be related to several parts of society, suchas 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 interestingto see how they influence each other on the amount of attention that is paid to this issue. Willan increase in attention of business men’s newspapers result in an increase of attention innewspapers that deal with popular issues; and how is this newspaper affected by a newspaperthat is more focused on scientific issues? In brief, How is the attention in a popularnewspaper caused by attention in scientific and economic newspapers. The most read popularnewspaper in the Netherlands is De Telegraaf, a newspaper that has a main financial orbusiness focus is Het Financieele Dagblad, and NRC Handelsblad is known for its relativelarge attention to scientific developments. The effects of both Het Financieele Dagblad andNRC Handelsblad are expected to be positive on the coverage of De Telegraaf. My hypothesisis 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.MethodIn order to investigate whether changes in the number of articles about sustainable developmentin NRC Handelsblad and Het Financieele Dagblad have an effect on De Telegraafs’s news, adataset was created via a computer-assisted content analysis, which was conducted using thedigital archive of the Web-based version of LexisNexis. Articles were selected via theBoolean 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 waschosen, because information about De Telegraaf is only available from 1999. The searchprocedure was repeated three times; one time for every newspaper, so three variables could becreated by aggregating the data on a weekly basis. A weekly basis is chosen, because it ismore detailed than the monthly basis, whereas a daily basis would lead to many days onwhich no coverage was found, what consequently meant that a lot cases had to be filled in byhand. A total of 35225 articles were found for 581 weeks; 18501 in Het Financieele Dagblad,10335 in NRC Handelsblad and 6389 in De Telegraaf. 1
    • To analyse the effects on the coverage of De Telegraaf, first an adequate ARIMAmodel is developed using Stata 10.1 for the time series of this variable, this was followed byadding a GARCH term to model the volatility, thereafter the independent variables wereadded to the model, resulting in a multivariate ARIMA model.ResultsIn this results section, I specify how the analysis was conducted and discuss the results thatwere found. I followed the ARIMA-framework described by Vliegenthart (n.d.) to make thebase ARIMA-model, thereafter GARCH-terms were added to take heteroscedasticity intoaccount and finally the independent variables were added to the model.ARIMA modelFigure 1 plots the time series of the attention in the three newspapers for the period that weare studying. It seems that Het Financieele Dagblad pays the most attention to sustainabledevelopment and De Telegraaf the least attention. The amount of attention seems to be risinga 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 thegraphs also show that there is some upward trend. Therefore, the data were fractionallyintegrated at a level of 0.352 following the Robinson (1995) multivariate estimate of the longmemory (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. 2
    • Table 1. The results of augmented Dickey-Fuller tests for the amount of articles over time Augmented Dickey-Fuller test Telegraaf FD NRCRandom walk without drift -6.560 -4.990 -5.596Random walk with drift -10.878 -10.104 -14.525Random walk with drift and trend -16.487 -15.716 -16.751 FI.Telegraaf FI.FD FI.NRCRandom walk without drift -11.756 -8.938 -10.011Random walk with drift -18.478 -17.020 -22.947Random walk with drift and trend -25.563 -24.102 -25.383Note. All tests indicate the absence of a unit root. FI, fractionally integratedThe next step was predicting the number of articles about sustainable development as good aspossible by accounting for its own past, either with autoregressive (AR) terms, movingaverage (MA) terms or both. This was done by inspecting the autocorrelation (ACF) andpartial autocorrelation functions (PACF). The ACF graph showed an unclear pattern, whilethe PACF graph displays a declining pattern for the first lags. This pattern is indicative for aprocess with a moving average at lag 1. A ARIMA (0,0.352,1) model seems thus the rightchoice. This model was tested for autocorrelation with the Ljung–Box Q test statistic and forthe presence of conditional heteroscedasticity with the Engle-Granger test. A significant resultfor the Ljung-Box Q-test for autocorrelation (20 lags) was found, meaning that the nullhypothesis of white noise was rejected and that the absence of autocorrelation cannot beassumed (Q = 807.40, p < 0.001). Therefore, to avoid autocorrelation in the ARIMA-model, itwas 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, itseems not possible to reduce the Ljung-Box test statistic Q2 based on the squared residuals toinsignificance, with AR or MA terms only. This means that there is a strong temporaldependency in the variance of the number of Telegraaf articles about sustainabledevelopment; heteroscedasticity. Residuals of the last ARIMA model were saved and are lateranalysed to see how the conditional variance of the number of articles in De Telegraaf wasaffected 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 theconditional variance of the dependent variable, either with autoregressive conditionalheteroscedasticity (ARCH) terms or with a combination of ARCH and generalizedautoregressive 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
    • Bayesian information criterion (BIC) (ΔAIC = 104.94, ΔBIC = 100.573). The results of thisgeneral model are showed in Table 2. The ARCH and GARCH terms are both statisticallysignificant and positive. This indicates that that innovations in the prior period increaseconditional variance in a next period. Periods of high volatility are thus likely to be groupedtogether in time. The autoregressive and moving average terms are also significant, meaningthat a particular number of articles in some week in De Telegraaf, are partly determined bythe 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 variablesConstant 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)aHet Financieele Dagblad (t - 1) 0.047 (0.023)*Ljung-Box Q(20) residuals 25.92 25.91AIC 3599.80 3590.38BIC 3630.34 3629.63Note. Unstandardized coefficients. Standard errors in parentheses;* p < 0.05 , a = 0.091Now a model was built that properly accounts for its own past and heteroscedasticity, theanalysis could go on with the next step: assessing the impact of the amount of news coverageabout sustainable development in NRC Handelsblad and Het Financieele Dagblad on that ofthe coverage in De Telegraaf. The cross-correlation function (CCF) for the residuals of thisGARCH model and for the amount of coverage in NRC, and the CCF for the residuals withthe coverage in Het Financieele Dagblad, indicate both that strong association is present whencoverage in both newspapers is lagged at 1 week. The results of the GARCH model thatincluded these two independent variables can also be found in Table 2. The results indicate that news coverage about sustainable development in HetFinancieele Dagblad (FD) had a significant positive effect on coverage about this issue in DeTelegraaf. A one article increase in FD, did on average result in a 0.05 article increase in thenext 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 isexpected to be positive, a one-tailed test can be used. Then the effect of NRC Handelsblad’s 4
    • coverage about sustainable development also becomes significant (χ2 = 2.85, p = 0.0456). Aone article increase about sustainable development in NRC Handelsblad, will on average alsoresult in a 0.05 article increase in De Telegraaf. Both effects seem thus to be rather weak.The conditional varianceAs written before, the ARIMA-model was highly volatile, meaning that the variance was notstabile over time. This heteroscedasticity could not be reduced by adding more autoregressiveor moving average terms, but a GARCH model had to be used. Though this heteroscedasticitywas unpleasant in the attempt to predict the numbers of articles published by De Telegraafabout sustainable development, it can also be used as interesting information. Consequently, Iwould like to know whether the conditional variance was affected by developments in thenumbers of articles published by the other newspapers. Therefore, the squared residuals of theAR(1)-I(0.352)-MA(1,2)-model were used as dependent variables. The time series of this variance-variable was stationary according to augmentedDickey-Fuller tests. Following the same framework (Vliegenthart, n.d.) as was done above, aARIMA(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 thevariance of the fractionally integrated number of articles in De Telegraaf. The next step wasto 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 thefractionally integrated values of the other two dependent variables at a lag of one week. Theresults 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 28.79Ljung-Box Q(20) residuals2 1.97AIC 7149.06BIC 7175.23Note. Unstandardized coefficients. Standard errors in parentheses;* p < 0.05News coverage about sustainable development in NRC Handelsblad does not influence thevariance of the fractionally integrated number of articles in De Telegraaf. Interestingly, this 5
    • variance was significantly and positively affected by news coverage in Het FinancieeleDagblad. This means that when the fractionally integrated number of articles aboutsustainable development in Het Financieele Dagblad increased, the variance in the number ofarticles in De Telegraaf also increased and it thus became more difficult to predict this valuesprecisely. The results of the ARIMA-model make clear that the variance on a certain momentis not strongly affected by previous variance, as both the AR and the MA-term areinsignificant.ConclusionThis study has found that changes in the number of articles about sustainable development inthe scientifically oriented newspaper NRC Handelsblad and the business oriented newspaperHet Financieele Dagblad, both lead to changes in the same direction in the number of articlesabout this topic in the popular newspaper De Telegraaf. A GARCH-model was used toanalyse 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 variableanother model was developed to predict volatility. The ARIMA-model that was built for thispurpose, found that variance could partly be predicted by the fractionally integrated numberof articles about sustainable development in Het Financieele Dagblad, but not by the coverageof NRC Handelsblad.ReferenceRobinson, 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 Filetsset week, weeklytwoway (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 driftdfuller Telegraaf*random walkdfuller Telegraaf, noconstant*trenddfuller Telegraaf, trend*with driftdfuller FD*random walkdfuller FD, noconstant 6
    • *trenddfuller FD, trend*with driftdfuller NRC*random walkdfuller NRC, noconstant*trenddfuller NRC, trendsearch ARFIMAroblpr Telegraafgen dfTelegraaf=Telegraaf-.3520017*l.Telegraafgen dfNRC=NRC-.3520017*l.NRCgen dfFD=FD-.3520017*l.FD*with driftdfuller dfTelegraaf*random walkdfuller dfTelegraaf, noconstant*trenddfuller dfTelegraaf, trend*with driftdfuller dfFD*random walkdfuller dfFD, noconstant*trenddfuller dfFD, trend*with driftdfuller dfNRC*random walkdfuller dfNRC, noconstant*trenddfuller dfNRC, trendac dfTelegraafpac dfTelegraafcorrgram dfTelegraaf*The ACF graph shows a clear spike a unclear pattern, while the PACF graphdisplays a declining pattern for the first lags.*A ARIMA (0,fi,1) model seems thus the right choicearima dfTelegraaf, ma(1)estat icpredict r, resgen r_s= r*rwntestq r, lags(20)wntestq r_s, lags(20)ac rpac rdrop r r_s*Q(r) and Q(r2) significicant, a peak at lag 2arima dfTelegraaf, ma(1 2)estat icpredict r, resgen r_s= r*rwntestq r, lags(20) 7
    • wntestq r_s, lags(20)ac rpac rdrop r r_sarima dfTelegraaf, ar(1) ma(1 2)estat icpredict r, resgen r_s= r*rwntestq r, lags(20)wntestq r_s, lags(20)ac rpac rdrop r r_s*Q(r) insignificant but Q(r2) significicantarch dfTelegraaf, ar(1) ma(1 2) arch(1)estat icarch dfTelegraaf, ar(1) ma(1 2) arch(1) garch(1)estat icdi 3704.739 - 3599.802di 3730.917 - 3630.344predict r, resgen r_s= r*rwntestq r, lags(20)wntestq r_s, lags(20)ac rpac rdrop 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 lagsfor NRC and FDarch dfTelegraaf, ar(1) ma(1 2) arch(1) garch(1)estat icpredict r, resxcorr r dfNRC, lags(13)xcorr r dfFD, lags(13)*both strongly correlate at the first lagdrop rarch dfTelegraaf l1.dfNRC l1.dfFD, ar(1) ma(1 2) arch(1) garch(1)estat icpredict r, resgen r_s= r*rwntestq r, lags(20)wntestq r_s, lags(20)drop r r_stest l1.dfNRCdi 0.0912/2*****Explaining conditional variance*****final arima modelarima dfTelegraaf, ar(1) ma(1 2)predict r, resgen sArima=r*rdrop rtwoway (tsline sArima, lcolor(black)) 8
    • *with driftdfuller sArima*random walkdfuller sArima, noconstant*trenddfuller sArima, trendac sArimapac sArimacorrgram sArimaarima sArimaestat icpredict r, resgen r_s= r*rwntestq r, lags(20)wntestq r_s, lags(20)ac rpac rdrop r r_sarima sArima, ar(1) ma(1)estat icpredict r, resgen r_s= r*rwntestq r, lags(20)wntestq r_s, lags(20)drop r r_sarima sArima, ar(1) ma(1)predict r, resxcorr r dfNRC, lags(13)xcorr r dfFD, lags(13)arima sArima l1.dfNRC l1.dfFD, ar(1) ma(1)estat icpredict r, resgen r_s= r*rwntestq r, lags(20)wntestq r_s, lags(20)drop r r_s 9