Example: The 2016 US presidential election and media on Instagram – who was in the lead?

This example is concerned with the number of candidate-related hourly media uploads to Instagram in the week before the 2016 US presidential election. Two prominent candidates were Hillary Clinton (Democratic Party) and Donald Trump (Republican Party). The election took place on Tuesday, 2016-11-08. While Hillary Clinton was widely expected to win, Donald Trump finally became the 45th president of the United States by winning the Electoral College.

Media on Instagram are annotated with hashtags which can be used to determine whether a candidate-related upload is neutral or in support of a candidate (for example, #makeamericagreatagain for Trump, #hillary2016 for Clinton) or opposing a candidate (for example, #dumptrump for Trump, #neverhillary for Clinton). In this way, four hourly time series were obtained: Trump pos/neutral and Clinton pos/neutral, the number of positive or neutral postings; and Trump neg and Clinton neg, the number of negative postings. For details, see our paper: Schmidbauer/Rösch/Stieler: The 2016 US presidential election and media on Instagram: Who was in the lead?, published in Computers in Human Behavior. The four hourly series of media uploaded to Instagram are shown here:

The following analysis (which can be reproduced with WaveletComp; all the commands are given in the guide booklet!) focuses on the week before the election: Sunday, 2016-10-30 23:00:00 EDT, through Sunday, 2016-11-06 23:00:00 EST; this is the shaded area in the plot above. The microstructure of the four hourly series becomes visible as we take differences:

There is obviously a 24-hour period in each of these series, reflecting Instagram users’ daily routine: busily posting media in the afternoons and evenings. Are there any other important constituents in these series? (In our context, this question means: Are there significant periods, other than the obvious 24-hour period?) Are the series in sync? (The answer to this question is relative to a period to be selected.) Is one series ahead of the other one, in our context: Was Clinton ahead, or was Trump ahead, or were they in sync? The cross-wavelet transform helps us answer these questions.

Now let's look at two pairs: Trump pos/neutral versus Clinton pos/neutral and Trump neg versus Clinton neg. Performing cross-wavelet transformation reveals that not only the 24-hour period is important, but the series in question also have a significant 12-hour period in common. This is hardly visible in the time series of differences! Then, who is leading?

The following plot shows the general scheme of leading and lagging time series. The series x and y have the same period. In the upper right quarter of the plot, x is leading because it attains its maximum before y. This is represented by an arrow pointing “north-east”. The other three cases are analogous.

With this scheme in mind, we see that Trump pos/neutral and Clinton pos/neutral are more or less in sync at the 24-hour period. However, Trump pos/neutral was leading over Clinton pos/neutral at the 12-hour period:

In the case of Trump and Clinton opponents, however, the relation at the 12-hour period was reversed:

It looks like Trump supporters and Clinton opponents were eager to post media, while Trump opponents and Clinton supporters were sluggish. In view of election forecasts and the age structure of Instagram users, these results come as a surprise. It can be shown with WaveletComp (see Section 7.3 of our guide booklet) that, at the 12-hour cycle, Trump supporters were on average 35 minutes ahead of Clinton supporters in posting media on Instagram in the week before the election, while Trump opponents were lagging on average about 22 minutes behind Clinton opponents. Why did this happen? Wavelet analysis cannot answer this question. However, with this evidence from wavelet analysis at hand, we can ask very specific questions.
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