Google Trends of political parties in Europe: a fractal exploration

Google Trends is a popular tool for exploring the online behavior of Internet users. One of the most prominent uses of the platform is for analyzing political trends, particularly in the context of elections and other political events. Despite its widespread use, however, there are a number of controversies surrounding the use of Google Trends data for political analysis. One of the main advantages of Google Trends is that it provides a large amount of data in real-time. By tracking the popularity of certain keywords and phrases, it is possible to gain insights into the interests and opinions of a given audience. This can be particularly useful for political analysis, as it allows researchers to track the popularity of different political parties and candidates over time. However, there are several limitations to the data provided by Google Trends. One of the main issues is that the data are based on Internet searches, which means that it is not representative of the entire population. Additionally, the data are not always accurate, as it can be influenced by factors such as Internet censorship and the use of VPNs (virtual private network) that mask the origin of searches. Despite these limitations, researchers have developed different techniques for analyzing Google Trends data in order to gain a more accurate understanding of political trends. One such technique is ARFIMA (Autoregressive Fractionally Integrated Moving Average) analysis, which is used to reveal previously non-evident relationships in the data.

The European Union, comprising 27 member states after the Brexit, has been characterized by a relatively stable political landscape in terms of the number of political parties present in its national legislative assemblies. This stability can be observed in the period from the financial crisis of 2008 to the present day. The financial crisis of 2008 had a significant impact on the political landscape of the EU (Hutter & Kriesi, 2019; Magalhães, 2014; Serricchio et al., 2013), with many member states experiencing a shift toward more populist and Eurosceptic parties (Dijkstra et al., 2020). For instance, in some countries like Italy and Poland, populist parties have gained significant support, while in others like Germany, the traditional parties have remained dominant. Despite this trend, however, the overall number of political parties present in the national legislative assemblies of the EU member states has remained relatively stable. This constancy can be attributed to certain reasons, including the proportional representation systems used in many EU member states which embody a given boundary for new parties to obtain full presence in these assemblies. That system is intended to avoid that a wide range of small parties could hinder the work of the assembly and prevent any one party from gaining a disproportionate amount of power. Another important factor is the presence of larger political coalitions or alliances at the national level. These coalitions or alliances provide a platform for parties from different ideologies to work together and pool their resources.

In this context, Google Trends is an interesting tool for exploring the public interest and awareness of political parties. By tracking search data, it is possible to identify changes in public attention and engagement with specific parties and individuals. Additionally, Google Trends data can be used to identify correlations between different political entities and to understand the key drivers of public interest. In addition to Google Trends, ARFIMA (Autoregressive Fractionally Integrated Moving Average) models can provide valuable insight into the underlying patterns and dynamics of political trends. ARFIMA models are statistical models that are used to analyze time series data, such as search data from Google Trends. ARFIMA is similar to ARIMA (Autoregressive Integrated Moving Average) technique, which is widely used since the 1970s, but it incorporates fractional integration that helps capturing long memory or self-similarity in the data. By analyzing the patterns of change in the data, ARFIMA models can identify underlying trends and patterns that would not be apparent from simple visual inspection or classic time series analysis. Despite the potential of combining the analysis of Google Trends with the capabilities offered by the ARFIMA technique, the authors are aware that the use of these data is not without controversy. Therefore, the present exploratory study and the results obtained from it must be approached with caution, as preliminary empirical insights would inspire further research. By applying ARFIMA to each time series, it will be possible to assign a decimal number to each political party, as a fingerprint, which will allow us to delve into their evolution, their similarities, and glimpse differences between the audiences who are interested in them through the searches. Among other variables, the country, the age of the political party since its foundation, and the political orientation will be explored to see if they can have a detectable effect on these search patterns and the predictable character of that online visibility.

The remainder of the paper is as follows: section 2 integrates relevant literature on the key aspects of the research, section 3 provides details on the econometric apparatus and data collection processes, section 4 offers and discusses empirical results, and finally, section 5 concludes and delivers some insights into policy implications.

The surge of Internet use in politics accelerated in the wake of the 2008 presidential elections in the United States of America, where candidate Barack Obama began to develop a novel Internet presence (Curran & Singh, 2011: 27; Gibson & McAllister, 2011: Gong, 2011: 307; 227; Huberty, 2015: 993). The Internet has become an increasingly important tool for political parties, both in general and in the context of the European Union. The ability for parties to be visible on the Internet, particularly through Google and other search engines, is seen as crucial for reaching potential voters and building support. With a majority of the population having access to the Internet, political parties are recognizing the importance of having a strong online presence in order to connect with potential voters. This includes having a well-designed website, having a strong social media presence, and appearing high in search engine results. Furthermore, the Internet has become a major platform for political communication and mobilization. Political parties can use the Internet to reach a wider audience and engage with potential supporters in ways that were previously impossible. This is why many parties are investing in online advertising and targeted campaigns to reach specific groups of voters. Moreover, the Internet provides new opportunities for parties to gather data and conduct research. By tracking online behavior and analyzing data, parties can gain insights into public opinion and voter preferences. This allows them to tailor their messaging and campaign strategies to better appeal to specific groups of voters. Citizens perform different searches of political terms or names of politicians on the Internet, which serves as the basis of an informed decision (Dylko, 2013: 65, Knobloch-Westerwick, Utych & Kam, 2013: 152–153). They inform and interact in the network by relying on the main search platforms that “have become an important part of the public dialogue” (Park, 2012: 680). It can be considered that searches for information about a particular candidate are motivated by a personal interest or by the consideration of a future vote (Wagner & Gainous, 2009: 507; Yasseri & Bright, 2014: 4)

Google is widely recognized as the leading search engine among Internet users, and it can be particularly relevant when it comes to searching for information about political parties in the European Union, as it is the preferred search engine by Western users (Urman et al., 2022). Considering its ease of use, accuracy and perceived relevance of results, and the wide range of information it provides, it is the preferred entry point for many individuals looking to access the websites and social media profiles of political parties in the EU, among other related political content. One of the key advantages of Google as a search engine is its ability to provide accurate and relevant results in response to user queries. This is achieved by advanced algorithms that consider a broad range of factors, such as the relevance of the webpage, the popularity of the site, and the keywords used in the search query. Furthermore, Google’s search results are often personalized, considering the user’s location, browsing history, and previous search queries, which makes it even more relevant to the user.

Despite the usefulness of these data set and techniques, however, there are several controversies surrounding the use of Google Trends data for political analysis. Some argue that the data are not reliable enough to be used for academic research, while others claim that the platform is biased toward certain political views. Furthermore, some researchers have raised concerns about the use of Google Trends data for political campaigning, as it can be used to target specific groups of voters. Although it is a widely used tool, researchers who use Google Trends to support their academic contributions have identified some disadvantages in its use. In the first place, when comparing the searches of terms in different states, we must not lose sight of the fact that Google as a reference search engine does not have the same implantation in each state and may distort the results (Jun, Yoo & Choi, 2018: 71). Second, and related to the previous question, Google Trends offers only Google search results. Third, the methodology used to show the results is not known (Mellon, 2013: 280, Reilly, Richey & Taylor, 2012: 152). Fourth, it cannot be checked by external agents. Fifth, it is not possible to precisely know the absolute number of selected searches (Olds, 2013: 264). Sixth, more transparency is needed in the data collection process (Huberty, 2015: 1005). However, along with these limitations, Google Trends has been widely used and “has been successfully expanded to various fields over the past decade” (Jun, Yoo & Choi, 2018: 80). Consequently, it is important to exercise caution when interpreting the findings of the current exploratory study. The results should be considered preliminary and exploratory in nature, serving as a starting point for further research. By utilizing the ARFIMA model on each individual time series, we will be able to assign a unique numerical value to each political party, effectively creating a “fingerprint” for each. This will enable us to delve into the evolution of each party, identify similarities and differences, and gain valuable insights into the interests and preferences of their respective audiences as reflected in online searches.

The year of foundation of a political party can impact its visibility on the Internet, particularly if it is younger or older than the financial crisis. Younger parties, for instance, may have the advantage of being founded after the widespread adoption of the Internet and social media, enabling them to leverage these technologies more effectively for their political goals. Additionally, younger parties may have had access to more funding for their campaigns and the development of their digital infrastructure, allowing them to establish a stronger online presence. Furthermore, younger politicians and activists may be more tech-savvy and comfortable with utilizing digital tools for political purposes, providing them with an edge in building an online presence. The financial crisis, which had a profound impact on many countries, also contributed to increased political and social polarization, changes in public attitudes toward politics, and a shifting political landscape. Younger parties may be better positioned to take advantage of these changes and establish a stronger online presence as a result. Finally, younger parties may have a more tech-savvy and digitally engaged target audience, which may be easier to reach and engage with through digital channels. The terms “ideological spectrum” and “political spectrum” are used to describe the range of political ideologies held by a political party. It is often represented as a numerical continuum that ranges from the left to right of the political spectrum, with zero being considered the center, negative values representing the left, while positive values represent the right (i.e., --2 Far-Left; −1 Left; 0 Center; 1 Right; 2 Far-Right). It is also interesting to check if that political orientation has also influence in their behavior as term of interest in Google. Furthermore, the European country in which a political party operates can significantly impact its visibility on the Internet. The availability of Internet access and the extent of Internet usage, for example, can widely vary between countries, affecting the reach of the party’s online presence. Moreover, the utilization of social media platforms can differ greatly between countries, impacting the party’s ability to connect with its audience through these channels. In addition, regulations and censorship laws surrounding the use of the Internet and social media can vary greatly, potentially hindering the party’s ability to spread its message and engage with its target audience online. Furthermore, cultural norms and values regarding the use of the Internet and social media can vary between countries, influencing the perception of the party and the extent to which its online presence is utilized. It is crucial to understand these elements to grasp the visibility of a political party on the Internet. All these characteristics of a political party, age, geographical space, and ideology contribute to their specific identity and hence could have an impact on their specific visibility. As stated by Milan (2015), the shift to a politics of visibility promoted by new technologies like – in his research – social media can have significant consequences in collective action.

In addition to our focus on analyzing dynamic web searches and interpreting them in political terms, there is a concern regarding the choice of methodological apparatus and the potential theoretical implications it may entail. There exists various mathematical models and techniques to create accurate explanations and predictions. Some authors argue that forecasting is based on the idea that the future is a singular, linear progression stemming from past events. There are a plethora of studies that utilize such models and even several researchers that use web search analytics as a source material for successful forecasting. The main mathematical models used in this research include time series algorithms such as (Autoregressive Integrated Moving Average) ARIMA, (Seasonal Autoregressive Integrated Moving Average) SARIMA, (Autoregressive Fractionally Integrated Moving Average) ARFIMA, as well as multivariate regressions and the (Autoregressive Moving Average with Exogenous Inputs) ARMAX model. It is important to note, however, that there is no one definitive method for determining which explanatory or forecasting technique should be used when analyzing a specific time series. In this exploratory work, a publicly available data set from Google Trends will be examined using the seasonal sARFIMA(p, d, q; P, D, Q) estimation model, as proposed by Granger and Joyeux (1980), which is also connected to ideas derived from chaos theory.

Our analysis centers on the idea of predictability. If the time series data collected from social phenomena follow the random walk hypothesis, then attempting to make explanations or predictions is unnecessary, as the current levels already reflect all available information and are subject to change with new information. However, if a certain level of predictability is possible, further questions arise: to what extent can reliable explanations and predictions be made? Are there effective ways to detect significant changes in the data? Are there long-term effects of certain events on the studied phenomena? This leads to the consideration of nonlinearity and the application of chaos theory, which suggests that a certain level of modeling and forecasting is possible. Another important concept in this context is self-similarity, as it allows for connections to be found across different geographic locations and time periods.

Chaos theory, first proposed by Lorenz in 1963, suggests that certain systems, while appearing random, may actually have underlying patterns and structures that can be identified and studied. One key concept in chaos theory is the idea of limited short-term predictability, which suggests that while it may be difficult to predict the exact outcome of a chaotic system in the long-term, it may be possible to make more accurate predictions in the short-term. Another important concept in chaos theory is self-similarity, which suggests that similar patterns and structures can be found across different scales and timeframes in a chaotic system. In this context, it is important to highlight that the application of these concepts can be used to study a wide range of different systems, including meteorology and other fields. Some details about this framework can be outlined: –

Lorenz’s model shows that complex behavior can have a hidden deterministic structure, revealed by simple equations given specific initial conditions and parameters. This new type of systems tends to be very sensitive to initial conditions; additionally, they have a long memory (persistence around a certain trend).

In this empirical paper, an exploration of the visibility of political parties via Google Trends is attempted, in order to contribute to this ongoing discussion. The present article complements this view using ARFIMA processes (Granger & Joyeux, 1980) instead of Hurst exponents (Hurst, 1951) to approach the fractal nature of the processes involved, as detailed in Flores-Muñoz et al. (2018)

Flores-Muñoz, F., Báez-García, A. J., & Gutiérrez-Barroso, J. (2019). Fractional differencing in stock market price and online presence of global tourist corporations. Journal of Economics, Finance and Administrative Science, 24(48), 194–204

Different methods are available for the analysis of relevant time series related to social phenomena. In recent years, given the inspiration of chaos theory, fractal geometry, and several other instrumental advancements, along with a significantly growing availability of data, this type of empirical study has suffered a significant development. Mandelbrot (1983) dimensions relate to time series analysis by means of long-run dependence systems or long memory processes. Thus, chaos theory concepts have a certain connection with a robust methodology for time series analysis: the Box–Jenkins methodology (1971) or the ARIMA estimation process. Abraham-Frois (1998) offers a didactic view of this connection, which is not free of controversy (Graves et al., 2017), and that is the view we follow here.

Let us consider y_t as a relevant time series for our purposes (i.e., Google Trends synthetic number). When running ARMA estimations, the first step is to evaluate if the series is stationary; that is, if the mean and autocovariances of the series do not depend on time. Therefore, the time series first needs to be differenced until it is stationary. The number of times the series needs to be differenced to achieve stationarity is reflected in the d parameter (Box & Jenkins, 1976). When d is allowed to be a non-integer, then the result is a fractionally integrated, autoregressive, and moving average estimation model (ARFIMA; see Appendix for some extra details on notation). Originally proposed by Granger and Joyeux (1980), the ARFIMA model follows the expression: (1) ϕp(B)(1−B)dyt=θq(B)εt {\phi _p}\left( B \right){\left( {1 - B} \right)^d}{y_t} = {\theta _q}\left( B \right){\varepsilon _t} or (2) (1−Σi=1p ρiBi)yt(1−B)d=(1+Σj=1q θjBj)εt \left( {1 - \Sigma _{i = 1}^p\;\;\;{\rho _i}{B^i}} \right){y_t}{\left( {1 - B} \right)^d} = \left( {1 + \Sigma _{j = 1}^q\;\;\;{\theta _j}{B^j}} \right){\varepsilon _t} where (1-B)^d allows for the fractional differencing of y_t in pursuit of stationarity, being ρ_i and θ_j, respectively, the p and q correspond to AR(p) and MA(q) estimations, B is the “lag” operator, and ε_t is the usual random residual. (3) Byt=yt−1;Bpyt=yt−p B{y_t} = {y_{t - 1}};{B^p}{y_t} = {y_{t - p}} (4) Bεt=εt−1;Bqεt=εt−q B{\varepsilon _t} = {\varepsilon _{t - 1}};{B^q}{\varepsilon _t} = {\varepsilon _{t - q}} Capital D, P, and Q are also added to account for seasonal effects, like in the classic ARIMA approach, being B^S such that B^sy_t = y_t-s, with s=13, 26, etc. in this paper with weekly data. (5) ϕp(B)Φp(Bs)(1−B)d(1−Bs)Dyt=θp(B)ΘQ(Bs)εt {\phi _p}\left( B \right){\Phi _p}\left( {{B^s}} \right){\left( {1 - B} \right)^d}{\left( {1 - {B^s}} \right)^D}{y_t} = {\theta _p}\left( B \right){\Theta _Q}\left( {{B^s}} \right){\varepsilon _t} As noted by Peters (1994), a non-integer value for d is connected to the concept of the fractal dimension D developed by Mandelbrot (not to be confused with the D for seasonal effects) as follows: (6) D=32−d D = {3 \over 2} - d The fractal dimension is related to a set of objects for which dimension is not an integer number, evolving from the classic Euclidean idea of dimension compared to the one studied in fractal geometry. Demand data series are among the candidates in the social sciences to be analyzed using this novel approach. The d parameter is also related to the popular Hurst exponent (Hurst, 1951), which is a measure of long memory in time series (Nile river behavior). This relationship allows researchers to establish certain boundaries, and to some extent decipher the behavior of the corresponding time series depending on the estimated d for the ARFIMA. The parameter d in ARFIMA models plays a crucial role in determining the memory and predictability of a time series. If 0 < d < 0.5, the time series has long memory, meaning that past values have a lasting impact on present values, leading to slow decay in the autocorrelation function. This type of time series is more difficult to predict, as the influence of past values will persist for a longer time. On the other hand, if 0.5 < d < 1, the time series has short memory, meaning that past values have a rapidly fading impact on present values, leading to a faster decay in the autocorrelation function. This type of time series is easier to predict, as the influence of past values will fade away quickly. In general, the closer d is to 1, the more predictable the time series will be. The precise interpretation of the d parameter and its effect on predictability will depend on the specific context and the application of the ARFIMA model. Some authors have proposed the existence of a relationship between memory and chaos in certain systems, so long-term memory in a time series could be related to the existence of certain chaotic patterns in its evolution.

Estimating d in a given social-related time series is relevant because, if significantly different from 0, it is related to long memory and to a certain degree of predictability. Additionally, the correct modeling of a time series allows for a more efficient detection of structural breaks. This is particularly interesting in political and social phenomena, which are subject to periods of instability, regular election processes, or the entry into force of new regulatory frameworks. We compare classic SARIMA processes with the corresponding ARFIMA ones. The comparison is made between the class of seasonal ARIMA models, SARIMA(p,d,q; P,D,Q), with an integer non-negative value of d, and the alternative given by the seasonal ARFIMA specification with a non-integer value of d. This study considers the analysis of weekly time series as provided by Google Trends, related to the four main political parties that are present in the corresponding national parliaments of the 27 member states of the European Union (EU). In order to have a complete comparison from political perspective, and given the strong interaction between the EU-27 and the United Kingdom along with the United States in almost any area of interest (defense, trade, science, migrations, …), the study also included the main political parties of both UK and USA. Only the two main parties were selected from USA because of the most prominent bipartisanship still present in that country. The sample period, organized in weekly data as provided by Google Trends, is April 2017 to April 2022, which means four series in each of the 28 countries plus the 2 time series for USA, including 261 observations in each time series, corresponding to 29,754 observations across the whole sample. This period of 5 years with weekly data is a standardized extraction by default from Google Trends as the authors considered a better solution for the replicability of the results. Additionally, that five-year period is strongly interested from a political point of view, including the political life of Donald Trump in the US, the role of Emmanuel Macron as President of France, and the consolidation of several new political parties in the corresponding European national parliaments since their birth as political movements derived from the financial crisis. This period also explicitly excluded the period of the invasion of Ukraine by Russia, which strong political implications could distort the present empirical experiment. Google Trends provides a synthetic artificial number that assigns the value of 100 to the week with the highest volume of search and rescales the rest of the weeks in proportion to that day. When inspecting a multitude of series, such as in the case of European political parties, it is not useful to compare relative volumes of searches. In this case, it is more useful to analyze other subtle elements such as trends or the fractal dimension that can be gleaned through the use of the ARFIMA technique.

Model selection is based on the usual test for individual significance of parameters (usual 1% and 5% levels), the normality of resulting residuals under Jarque–Bera test, and the global significance of the model using F statistics along with minimizing information criteria among models. Estimation of d was performed using EViews9 (based on Sowell, 1992; Doormik & Ooms, 2003). Estimation was performed using the standardized Maximum Likelihood (ML). For ARFIMA estimation, the fractional difference parameter is initialized using the Geweke and Porter-Hundlak (1983) log periodogram regression (Automatic), with a fixed value of 0.1. The information matrix estimate is computed using the outer product of the gradients (OPG). The optimization algorithm included in Eviews is also based on the Berndt–Hall–Hall–Hausman (BHHH) algorithm. At the time of this writing, this software does not offer the technical capabilities to perform fractional D (for the seasonal component), so D remains integer in both SARIMA and seasonal ARFIMA specifications, with D=13, 26 in several estimation models (weekly data). This is a limitation of this empirical work that will be overcome in future research. This research contributes to the literature because it shows the potential of a new tool for the analysis of relevant time series to monitor the behavior of political processes.

Once the fractal dimension and other estimation parameters of each of the analyzed series are obtained, it will be possible to group them using common techniques such as cluster analysis. This will allow grouping the search trends and thus verifying if they align based on certain variables such as geographic location or political alignment of each of the parties whose series the parameters correspond to. Cluster analysis is a useful tool for grouping time series data as it allows for the identification of patterns and similarities within the data. By grouping similar time series, it is possible to identify common trends and patterns, which can provide valuable insights into the underlying processes that generate the data. Additionally, cluster analysis can be used to identify outliers or anomalies within the data, which can be useful for detecting and addressing potential issues or errors in the data. Overall, the use of cluster analysis in time series data can greatly enhance our understanding of the underlying processes and trends within the data.

The first stage of the analysis refers to the values obtained for the fractal dimension d in the different parties. A first impression, offered in Table 1, is that the values of the estimated d are consistent with what is expected for the systems described previously. The time series seem to present “long memory” as the obtained values are in the interval 0 < d < 0.5, which means that earlier values continue to affect current values to a significant extent, resulting in a gradual decrease in the autocorrelation function. This makes the time series harder to predict, as past values will continue to play a role for an extended period of time.

Table 2 presents an ordered list of the d estimates, and it is clearly apparent that the location of each political party within a specific country is a factor that must be given due to consideration. The countries with the largest economies have been emphasized to show that they are spread out along the ordered list rather than concentrated toward high or low values of d.

The year of foundation of each political party appears to have a minor effect on the differentiation of the d estimate, leading to lower predictability in both very old parties (19th century) and very new parties (established post-financial crisis), and higher predictability among parties founded in the first half of the 20th century (Table 3).

Table 4 does indeed reflect a decreasing order in the average d estimates, when they are ordered according to the political ideology scale described previously. There is higher predictability in the time series related to the political on the left and somewhat lower predictability on the right.

In order to complete the analysis, the cluster method will take into account the categorical variables of political ideology of the parties and the belonging of the countries to one of the two blocks, Western Europe (capitalist) and Eastern Europe (communist), which formed the old dichotomous political division in which Europe was divided. Ideology is a relevant factor when making a separation in behavior, especially in a world like today’s where social networks filter the speeches that citizens receive and reinforce one ideology or another with interests of various kinds, whether commercial or political. The adherence of countries to one of the two political blocks formed after II World War also seems to be a relevant factor in behavior, as in the period of greatest growth and splendor of the countries, they lived from opposite ideologies and political forms, which created a completely different life experience and socialization in the over 30 years that this political division lasted. And although over the years all these countries have adopted the market economy and parliamentary democracy as a form of government, it is still very likely that the political origin will continue to be a differentiation factor. As quantitative variables, data from the fractal value d and r² of the ARFIMA (fractionally integrated ARIMA) stochastic models derived from the analysis of the time series of political party searches will be considered. In Table 6, the summary of the model of the first cluster analysis is outlined. It is a two-stage cluster analysis, using log-likelihood as a distance measure and the Akaike information criterion as a clustering criterion. Three input variables are used, 2 qualitative or categorical variables are used, and 1 quantitative or continuous variable is used. The categorical variables were rearranged to express ideological inclination (4 categories) and the political block after the 2nd World War (2 categories). As a continuous variable, the fractal value derived from the ARFIMA models is used.

The cluster analysis of the first model has good discrimination between clusters, observing a measure of separation and cohesion silhouette with a value of 0.5, and it has identified 7 clusters with the clustering criterion used. These clusters belong to each of the ideologies with each of the political blocks, so the analysis determines that the fractal values of the ARFIMA models show clustering criteria regarding the ideology of the political party and the block to which they belonged after the II World War. In the detail of the data of the clusters (Table 6), two of the largest are observed (Centre-Right and Western Europe [23.2%] and Centre-Left and Western Europe [20.5%]), two intermediate (Right and Western Europe [16.1%] and Centre-Right and Eastern Europe [15.2%]), and three of smaller size (Right and Eastern Europe [9.8%], Left and Western Europe [8.9%], and Centre-Left and Eastern Europe [6.2%]). The political ideology variable of the parties is the one that has the greatest importance when forming the clusters.

In Table 7, the summary of the second cluster analysis model is also offered. This is also a two-stage cluster analysis, with log-likelihood as the distance measure and Akaike as the grouping criterion. Three input variables are also used, two of which are qualitative or categorical and one is quantitative or continuous. The categorical variables are the same as those used in the previous model (ideological inclination and the political bloc after II World War). In this case, the r² value of the ARFIMA models performed with the data of political party searches in Google Trends is used as a continuous variable.

This second analysis has a good discrimination between clusters, being better than in the previous case, by obtaining a higher separation and cohesion measure, with a value of 0.6 compared to 0.5 of model 1. Seven clusters have also been identified with the grouping criterion used and follow the same criteria, where each cluster belongs to each of the ideologies with each of the political blocks. This analysis determines that the values of r² of the ARFIMA models show grouping criteria regarding the ideology of the political party and the block to which they belonged after II World War, and, therefore, the predictive value of said ARFIMA models is related to it. The size of the clusters and the variable of greatest importance (the ideology of the political parties) are the same as in the previous model.

The Internet has ushered in a new era of interpersonal political communication, marked by an unprecedented level of citizen participation. Political actors, quick to recognize the opportunities presented by this digital landscape, have strategically leveraged their online presence. The profound impact of this shift on politics is undeniable. This evolving channel of communication and engagement, where various political formations and leaders actively seek to enhance their connections with the electorate, amplifies the reach and resonance of their messages. In parallel, citizens exhibit a growing interest in political parties that consistently navigate the complexities of contemporary times, maintaining a robust presence in public life. The conduit for this interaction is the Internet, with popular search engines such as Google serving as gateways to the web pages and social media profiles of these political entities. Our exploratory study suggests that during these searches, Internet users leave a discernible digital footprint that statistical techniques can detect. This opens avenues to infer distinctions among Internet users, unveiling potential geographical or political alignment differences.

Building upon the groundwork laid by Beyer (2012), future research extensions should explore the temporal dimension as a crucial factor in political analysis. Integrating time sequencing into political reform efforts warrants empirical studies akin to the present one, which focuses on time series exploration. Such studies prove instrumental in comprehending the evolving dynamics of political engagement. This exploratory study serves as a foundation for subsequent research into the nature of these identified differences. Understanding the predictive potential of this public data becomes paramount, especially concerning its applicability in political consulting and analysis. As we delve deeper into more sophisticated analyses, adopting techniques like breakpoint detection, as demonstrated in the work of Mora et al. (2021), represents a logical progression. This would provide a more nuanced understanding of the underlying patterns and trends in political communication and citizen engagement, enhancing our ability to shape effective policies and strategies.