Forecasting fertility is a key element in the development of medium- and long-term strategies for socio-economic development and demographic policy in any country. Fertility forecasts are necessary for assessing the future balance of labour resources, planning the development of the social sphere, and determining needs for medical care, social services, and other areas. International organizations use various methodologies to construct fertility forecasts, including cohort-component models, stochastic models, probabilistic methods, and others. The choice of methodology depends on the quality and availability of source data across countries and regions, as well as on the need to account for specific demographic characteristics, economic and social conditions, the impact of crises, migration, and other factors. Variations in forecasting methods are also associated with different levels of detail and forecast objectives, which may serve as a basis for policy development or academic research [Kishenin 2023]. Demographers note that a universal approach to fertility forecasting that adequately reflects global and regional differences has not yet been developed [Soroko 2018].

In the Russian Federation, econometric models have recently been increasingly used to forecast demographic indicators, including mortality [Gusev et al. 2023], the seasonality of mortality among children and adolescents [Kuznetsova and Maleva 2022], and losses associated with obesity and overweight [Kuznetsova 2025], among others.

In recent decades, with the development of the internet and the digitalization of the economy and society, a large volume of information related to social media use, website activity, search engine data, SIM card mobility data, and other digital traces has emerged. Until recently, such digital information was rarely used in academic economic research, with preference traditionally given to classical sources of official statistical data. Over the past decade, however, interest in digital data – particularly search query statistics – has increased in both international and domestic research. For example, Jun et al. [2018] conducted a review of 657 articles from various fields that used Google Trends data, highlighting the growing popularity of digital data sources.

By combining data from search engines with official statistics, it is possible to obtain a more comprehensive understanding of demographic processes, both in terms of overall trends and the mechanisms underlying their formation, which is especially important in the context of contemporary uncertainty. Alongside classical econometric approaches to forecasting the dynamics of economic and demographic processes – which tend to perform well under conditions of stable underlying trends – forecasting based on search query data is increasingly being applied, as it can improve forecast accuracy.

It is also important to note that internet search queries and search behavior can serve as unique indicators of changes in social behavior, capturing population intentions, sentiments, and preferences in response to changing conditions during periods of uncertainty (such as pandemics, economic crises, and military conflicts) well before the publication of official statistics, or in contexts where the dissemination of demographic data is restricted. For example, increased interest in topics related to pregnancy and childbirth may precede an increase in fertility, signaling shifts in reproductive intentions with a lag of approximately nine months prior to the release of official statistics.

This article examines the possibilities and limitations of using search query statistics to forecast fertility in Russia.

Over the past decade, the use of web-based data in scientific research has demonstrated its usefulness for assessing various aspects of human activity. Google Trends is the most widely used tool for collecting such information. One of the pioneering studies on the use of Google Trends for forecasting was conducted by Ginsberg et al. [2009], who showed that Google Trends data could track and predict the spread of influenza more rapidly than reports from the Centers for Disease Control and Prevention (CDC).

Mavragani et al. [2018] provided an analysis of 109 articles published between 2006 and 2016 that used Google Trends for forecasting public health processes, with a focus on interest in different aspects of healthcare systems, public responses to epidemics, and seasonal patterns of diseases and health-related problems. Google Trends data has also been widely applied in forecasting economic indicators, including GDP growth in the United States [Kohns et al. 2023], unemployment rates [Askitas 2009], exchange rates [Bulut 2018], levels of economic activity (such as car sales, housing sales, retail trade, and travel behavior) [Choi and Varian 2012], as well as demographic indicators [Billari et al. 2013; Ojala et al. 2017; Jurić 2021; Wilde et al. 2024].

In Russia, some experience has also been accumulated in using search query statistics to forecast economic and demographic indicators, including the unemployment rate [Yurevich and Akhmadeev 2021], macroeconomic variables [Borochkin 2013], birth and marriage rates [Kalabikhina et al. 2020], migration [Bronitsky and Vakulenko 2022; Fantazzini 2021; Bronitsky and Vakulenko 2024], household deposit outflows [Gurov et al. 2023], economic agent sentiment [Petrova and Trunin 2020], and bitcoin volatility [Teterin and Peresetsky 2024], among others.

New digital data sources, such as Google Trends and Yandex Wordstat, have expanded the possibilities for demographic analysis. These tools are used to address a wide range of research tasks, from improving demographic forecasts to analyzing public sentiment and identifying the reproductive attitudes of the population. Google Trends provides statistics on Google search queries starting from 2004, while Yandex Wordstat has offered statistics on Yandex search queries since 2018. Search queries constitute a valuable data source, as they consist of anonymized information generated by large groups of users.

The use of Google Trends and Yandex Wordstat data has several advantages, including accessibility, large data volumes, and geographic detail. A number of studies confirm that search activity is closely linked to reproductive behavior and family planning. For example, positive correlations have been found between the number of births and Google Trends search queries related to “motherhood,” “ovulation,” and “pregnancy” [Billari et al. 2013], “pregnancy” [Kalabikhina et al. 2020], as well as “conception” and “pregnancy” [Wilde et al. 2020]. Wilde et al. [2020] also demonstrate that the use of search query statistics made it possible to predict a 15% decline in births in the United States due to the COVID-19 pandemic and to improve forecast accuracy by approximately 25%.

Forming a set of search queries plays an important role when working with search data. For example, in studies on fertility [Billari et al. 2013; Kalabikhina et al. 2020], the query set is formed by selecting relevant keywords in Google Trends. An expert-based approach is often used, involving the construction of thematic query blocks, such as “Early indicators of pregnancy” and “Unemployment” [Wilde et al. 2020], or “study,” “work,” and “embassy” in migration studies [Bronitsky 2024].

In addition, modern methods for forming query clusters are applied, including the identification of “synsets”¹ based on keywords using WordNet² [Avramescu and Wiśniowski 2021], as well as the application of machine learning methods and natural language processing (NLP)³ approaches based on text corpora [Bronitsky and Vakulenko 2022]. At the keyword selection stage, the choice is most often made based on correlation with the dependent variable, following a series of validation procedures, including sample size assessment, evaluation of correlation with the explanatory variable, and cross-validation with MAPE minimization.

Let us note several general points regarding the reviewed studies. First, most authors emphasize that the use of search query data improves the predictive performance of models compared to classical approaches. Second, the approaches used to generate the set of search queries subsequently incorporated into forecasting models vary substantially across studies, ranging from the selection of phrases logically related to the object of analysis to the application of machine learning methods. Third, there are very few studies devoted to forecasting fertility in Russia using Google Trends data and time series models.

It should be noted that Kalabikhina et al. [2020] use a limited set of search queries when forecasting fertility, with only a small number of queries selected using an expert-based approach (“engagement ring,” “pregnancy,” “abortion,” “registry office,” “maternity hospital,” and “divorce documents”). In the present paper, the set of search queries is expanded using machine learning methods.

When forecasting processes based on search query statistics, various econometric models are employed, including VAR models [Adu et al. 2023] and Bayesian models [Kohns et al. 2023]. However, ARIMA and SARIMA class models are used more frequently, depending on the indicator, due to their ease of implementation and the reliability of the resulting estimates. These models are typically adopted as baseline specifications that do not include search query statistics as explanatory variables and are used for comparison in order to assess the extent to which the inclusion of search query data improves forecast accuracy.

Search queries are incorporated into forecasting models in different ways. For example, in Billari et al. [2013], search queries enter an ARMAX model as exogenous variables and influence fertility forecasts. Bronitsky [2024] compares a SARIMAX model that includes a single exogenous variable (and its lags) with a distributed lag model that incorporates several search queries. The results indicate that during periods of external shocks, the distributed lag model exhibits higher forecasting accuracy.

An important feature of working with time series data is the inclusion of lagged values of search queries, with lag lengths varying depending on the research topic. For instance, when forecasting migration, lags from 1 to 12 months are typically used [Bronitsky 2024]; for forecasting the number of births, lags range from 7 to 12 months [Wilde et al. 2020]; and for unemployment, lags of 1 to 4 months are applied [Yurevich and Akhmadeev 2020].

Number of births. The study uses time series data obtained from the Unified Interdepartmental Information and Statistical System (EMISS)⁴. The monthly number of registered births in the Russian Federation for the period from January 2006 to December 2024 is examined (Fig. 1). The time series exhibits a pronounced parabolic trend and clear seasonality with a 12-month periodicity. It should be noted that during the period from 2006 to 2014 there was a steady increase in the number of registered births in Russia; after 2015, a downward trend emerged, reaching a minimum of approximately 95 thousand births.

Based on the HEGY test (specifications with a constant; with a constant and trend; and with a constant, trend, and seasonal dummies), the stationarity of the series was tested, taking into account the seasonal nature of the data. At the 5% significance level, the orders of non-seasonal and seasonal integration of the process were determined. The series of registered births became stationary after applying both non-seasonal and seasonal differencing.

Search query statistics were constructed using the Google Trends Index⁵ (hereinafter GTI). Google Trends is a platform that provides time series of search queries reflecting the dynamics of user interest in selected keywords. The main metric of search query frequency is the relative share of queries, calculated as the ratio of the number of searches for a specific keyword to the total number of searches in a selected region over a given period. The platform allows filtering by geographic location, time frame, subject category, and search type. In this study, web search data restricted by country and time period are used.

A key limitation of Google Trends is that the relative share of queries is presented in normalized form, which complicates comparisons across different time periods. The same query may have different index values depending on the selected time window, and absolute numbers of queries are not available. To address this issue, the GTI data were subsequently standardized, following Fantazzini [2021] and Bronitsky and Vakulenko [2024]. Another limitation is the change in Google’s data collection and processing methodology in 2011, which affected index calculations and makes data prior to 2011 incomparable with later observations. Therefore, only data from 2011 onward are included in the analysis.

To ensure comparability between the baseline models and the extended models incorporating search data, all SARIMA and SARIMAX modelsare estimated using data starting from January 2011. Accordingly, the GTI search query time series⁶ analyzed in this study cover the period from January 2011 to December 2024.

As an example, Fig. 2 shows the time series of the search query “Pregnancy.”

It can be observed that the series exhibits both a trend and a seasonal component. Therefore, for subsequent fertility forecasting using SARIMA models, it is necessary to examine the stationarity of each query and determine the appropriate model parameters. Each query variable was tested for stationarity using the HEGY test, with results presented in Appendix (Table A2). Based on the test, the orders of non-seasonal and seasonal integration for SARIMA were determined: ddd and DDD, respectively. The t1 statistic corresponds to the hypothesis of the presence of a non-seasonal unit root in the test equation, while the F1 statistic corresponds to the hypothesis of a monthly seasonal unit root. Some series were stationary at levels (d = 0). When necessary, non-seasonal and seasonal differencing was applied to bring the series to stationarity, according to the test results.

When using GTI statistics for forecasting, it is necessary to identify a set of relevant search queries. Several approaches can be used to form such a set, one of which is expert selection, including relying on previous research. Thus, the initial list was compiled based on topics identified in scientific publications, such as “pregnancy” and “maternity hospital” [Kalabikhina et al. 2020], “childbirth” [Ojala et al. 2017], “pregnancy test” [Jurić 2021], as well as “pregnancy symptoms” and “pregnancy vitamins” [Wilde et al. 2024].

A distributed word embeddings approach was also applied to generate an extended set of fertility-related search queries. Using a machine learning model trained on a corpus of Russian-language texts, including Wikipedia articles, dictionaries, and other corpora, semantically similar words were extracted from the initially expert-defined set of terms. Semantic similarity was measured as the cosine similarity between word vectors, ranging from 0 to 1 (0 indicates no similarity; 1 indicates complete coincidence in context and meaning). In practice, cosine similarity values above 0.5 are generally considered indicative of a meaningful semantic relationship, while values above 0.7 indicate a high degree of similarity in context. In this study, words with similarity greater than 0.5 were selected.

For example, a model trained on Russian-language Wikipedia identified the terms “menstruation” (0.66), “give birth” (0.61), and “ovulation” (0.6) as closest to the word “pregnancy.” However, not all resulting phrases correspond to actual user behavior online. A term may be linguistically close in meaning but rarely used in real search queries. For instance, the model recognized “pregnancy test” as similar to “pregnancy diagnosis” (similarity = 0.5). However, “pregnancy diagnosis” is rarely searched by ordinary users and is more typical of professional terminology. Consequently, insufficient GTI data are available for such queries, limiting their usefulness in modeling.

The second method is based on statistics of word usage on the Internet. One of the online platforms providing such statistics is the National Corpus of the Russian Language (NCRL)⁷. This is a large collection of Russian texts, including fiction, journalistic, scientific, and colloquial materials. The NCRL contains texts from various historical periods and genres, all annotated linguistically, allowing the study of word frequency, grammatical characteristics, contexts of use, and linguistic changes.

Currently, the NCRL contains approximately 342 thousand texts and over 2 billion words. Various linguistic metrics are employed to analyze relationships between words. In addition to simple frequency counts, statistical measures such as Mutual Information (MI), Log-likelihood, T-score, LogDice, and aggregate measures are used. These metrics help determine how often words co-occur and the strength of their semantic relationships. For example, LogDice identifies stable and meaningful phrases, while MI highlights rare but semantically significant word pairs.

For the selection of collocations⁸, an aggregate measure – representing the geometric mean of the T-score and MI measures – was used for many search queries. This approach allowed consideration of both the strength of association and the stability of phrases within the corpus. For example, for one of the collocates of the word “pregnancy,” namely “trimester,” the following metrics were obtained: MI = 14.15, Log-likelihood = 158.96, T-score = 3, LogDice = 8.82, and aggregate measure = 6.52. These values indicate that this is not a random co-occurrence but a stable lexical collocation; that is, “pregnancy” and “trimester” frequently appear together. Other collocates include “fertility,” “motherhood,” and “midwife.”

As a result, for each approach, an initial set of 67 search queries was defined. This set was subsequently reduced to 56 queries due to insufficient data for some terms, which were then used to extract the GTI time series. Thus, 56 words and phrases were included in the final set of search queries, distributed across four thematic blocks related to reproductive behavior: “pregnancy planning,” “pregnancy course,” “preparation for childbirth,” and “universal queries” relevant at any stage (see Table 1).

In order to use the obtained search queries in time series forecasting models, it was necessary to significantly reduce the dimensionality of the query set. Estimating a SARIMAX model with 56 variables included as exogenous regressors is not feasible due to the limited length of the birth number time series and the difficulty of interpreting such a high-dimensional multivariate model. Following the approach of similar studies [Yurevich and Akhmadeev 2020; Bronitsky 2024], principal component analysis (PCA) was used to reduce dimensionality. PCA was applied both to the entire set of queries and within each thematic block.

Initially, PCA was applied to the full set of 56 search queries. However, using the Kaiser criterion (eigenvalue > 1), 19 components were extracted, which was still too many for further analysis. Therefore, PCA was subsequently performed separately within the pre-defined thematic blocks of queries based on substantive similarity. The analysis by thematic blocks yielded the following results according to the Kaiser criterion (see Table 2):

For the subsequent analysis, principal components were used instead of the original search queries.

The SARIMA model was used as the baseline model for the time series covering the period from January 2011 to December 2024. Based on the information criteria AIC and BIC, the most optimal model was identified as SARIMA (2, 1, 0)(0, 1, 1)₁₂:

(1 – φ₁L – φ₂L²)ΔΔ₁₂y_t = (1 + θ₁₂L¹²)ε_t, (1)

where φ_i are coefficients of the AR part, L is the lag operator (L^ky_t = y_t−k), Δ = 1 − L is the first non-seasonal difference operator, Δ₁₂ is the seasonal difference operator, θ_i are the coefficients of the MA part, ε_t is white noise Parameter estimates for model (1) are provided in Appendix (Table A1).

To verify the assumptions of the model and assess the adequacy of the estimates, the residuals were analyzed for autocorrelation and conformity with the normal distribution. The residuals were found to be consistent with a white noise process, as indicated by the Ljung – Box statistic⁹ (Q-stat = 0.07, p-value = 0.79) and Jarque – Bera statistics (JB = 2.79, p-value = 0.25). The baseline SARIMA model was then extended to a SARIMAX model, in which principal components (PCs) of the thematic blocks, with appropriate lags, were included as exogenous variables.

Initially, an increasing number of components were sequentially included in the SARIMAX model for each thematic block. The resulting models were then compared using the Akaike Information Criterion (AIC), and for each block, the number of components was selected for which the model exhibited the lowest AIC value. The selection was performed separately for each block, and only statistically significant principal components were included (see Table 2).

Taking into account the lag structure of data. The next step in modeling involved introducing a lagged component structure, as it is reasonable to assume that the influence of interest in certain topics (search queries) on the birth rate may manifest with a delay of varying length. Based on the literature review, lags from 1 to 12 months were considered. This range corresponds to the plausible time between interest in fertility or childbirth topics and the actual realization of reproductive intentions.

Lags were selected based on the analysis of cross-correlation functions between the differences in principal components and the target variable – the number of births. The final model included only those lagged PCs that were statistically significant. Lag lengths varied from 1 to 12 months depending on the thematic block.

For example, in the “Preparation for Childbirth” PC block, 17 lags were included in the model. By component:

A detailed list of lags for each thematic block used in the SARIMAX models is provided in Appendix (Table A3).

The lag structure of the models proved to be complex and difficult to interpret. To assess the stability and adequacy of the lag structure, the average lag was calculated for each thematic block, following the methodology proposed by Bronitsky and Vakulenko [2024]. The results of the average lag estimation, with 95% confidence intervals, are presented in Table 3.

The “Universal queries” block showed the smallest average lag, 5.3 months, with a 95% confidence interval of [3.31; 7.66], indicating the shortest time delay between search activity and the corresponding births for this thematic block. The “Planning” block exhibited the largest delay, with an average lag of 7.4 months [5.65; 9.19]. Comparison of the average lags for the blocks “Planning,” “Pregnancy Course,” and “Preparation for Childbirth” shows a decreasing trend: 7.4, 6.6, and 6 months, respectively. This pattern is consistent with the logical interpretation of the principal components: from pregnancy planning to childbirth, the expected lag decreases. These results further confirm the adequacy and stability of the proposed SARIMAX-based forecasting method with the selected lags.

Comparison of forecast quality. When constructing demographic forecasts, the accuracy of the resulting estimates is of primary importance. In this section, we analyze forecast accuracy depending on the selected model. Table 3 presents the results of assessing the quality of fertility forecasts based on different models: the baseline SARIMA model without search queries, SARIMAX models with principal components (PCs), and SARIMAX models with PCs including the lag structure.

The metrics used to evaluate forecast quality were the mean absolute percentage error (MAPE) and the mean absolute error (MAE), calculated over forecast horizons of 1, 2, and 3 years.

The results show that including components obtained through PCA leads to a significant improvement in forecast accuracy compared to the baseline SARIMA model, which does not include search data. For instance, the baseline SARIMA model had a 1-year MAPE of 4.62%, whereas using PCs from the “All queries” block without lags reduced the error to 3.2%. The greatest improvement, however, was observed when incorporating the lag structure (PCs from the “Preparation for Childbirth” block): in this case, MAPE decreased to 3.1% and MAE to 3,120.7, reflecting the time lag between user behavior online and subsequent demographic responses.

The largest effect of adding PCs and lags among thematic groups was observed in the “Preparation for Childbirth” and “All queries” blocks. Using two components from the “Preparation for Childbirth” block while accounting for lags produced the best results among all tested models: the minimum errors were 2.71% for MAPE and 2,816.9 for MAE over a 3-year forecast horizon. This suggests that the “Preparation for Childbirth” query block is directly related to imminent births, as it includes queries from women who are already aware of an upcoming birth and are actively preparing. This block reflects the actual “activity” of pregnant women, rather than mere interest in the topic, when intentions to give birth may not yet be realized. Such data provide a clear and timely signal for short-term forecasts.

When using all blocks together, some queries may be indirect (e.g., “Planning,” “Other”) and introduce noise, reducing short-term forecast accuracy. Although the “All queries” block sometimes shows slightly lower error metrics, the large number of components and lags reduces the number of observations available for model estimation, complicating robustness testing.

These results confirm the high predictive value of queries related to preparation for childbirth (e.g., maternity hospital, hospital bag, breathing during childbirth). In other blocks, such as “Pregnancy Course” and “Universal Queries,” the addition of components and lags also improves forecast quality, but the effect is less pronounced.

The results of the three-year forecast of the number of births are presented in Fig. 3.

The red and green lines in Fig. 3 show the predicted number of births according to the SARIMA model (without search queries) and the SARIMAX model (with search queries and lags) for the control period from 01.01.2022 to 01.12.2024. It is evident from Fig. 3 that the model incorporating search queries and lags better captures the dynamics of the observed process.

To assess the robustness of the forecast quality metrics, two types of cross-validation¹⁰ were additionally performed: with an expanding window and a sliding window, for forecast horizons of 1, 2, and 3 years. The window width varied from 60 to 96 months¹¹. The MAPE values are presented graphically in Appendix (Fig. A1-A2).

For the baseline SARIMA model (without queries), MAPE ranged from 4.27–4.76% for the sliding window and 3.99–5.17% for the expanding window. For the best-performing model (with search queries and lags), MAPE ranged from 3.11–4.37% for the sliding window and 3.04–3.63% for the expanding window. These results confirm that including search queries improves model accuracy and demonstrates the robustness of the findings.

Furthermore, in all models, there is a consistent decrease in error values (i.e., an increase in forecast accuracy) for both MAPE and MAE as the forecast horizon increases from 1 to 3 years.

Since the MAPE quality metrics showed a substantial decrease, it was important to assess the statistical significance of these changes. To this end, the Diebold-Mariano test was conducted to evaluate whether the differences in forecast accuracy between the models were statistically significant, compared to the baseline SARIMA model without search queries (see Table 4).

In this test, the null hypothesis assumes no difference in forecast accuracy between the compared models and the baseline model.

Cases in which the forecast quality metrics of the extended model statistically outperform the baseline SARIMA model according to the Diebold–Mariano test (with p < 0.1) are highlighted in bold. Values are reported as: DM statistic (p-value).

The results presented in Table 4 indicate that all models incorporating search queries outperform the baseline SARIMA model in terms of forecast accuracy. The largest improvement was observed for the model using the “All queries” principal components while accounting for lags.

Forecasting horizon. The study revealed an interesting pattern across all models: as the forecast horizon increases from 1 to 3 years in the SARIMA/SARIMAX models, forecast accuracy improves. This may be due to the fact that one-year forecasts are more sensitive to random short-term factors, such as extreme events or anomalies, which are not captured by the model. In contrast, three-year forecasts tend to average out the effects of short-term noise and better capture seasonal cycles and underlying trends, as seasonal patterns become more pronounced and stable over longer horizons.

Inclusion of search queries in the models helps to clarify these trends and strengthens the significance of identified dependencies, thereby improving the accuracy of long-term forecasts. Although the differences in quality metrics are relatively small, this finding may prove valuable for developing population projections using SARIMAX models.

This study did not account for regional differences in population search activity. It can be assumed that the results may vary when moving to the regional level or when forecasting for a specific region.

The stability of the influence of multiple search queries, as well as their dimensionality and composition, was beyond the scope of this study and remains an open question.

Additionally, during different periods – particularly during times of uncertainty, such as pandemics, military conflicts, or economic and political instability – search queries may influence birth rates differently, with varying lags and significance of individual components. This aspect was not addressed in the current study and will be the subject of further research.

This article examined a method for forecasting the birth rate in Russia using Google Trends Index (GTI) search query statistics. The results demonstrate that incorporating search queries and their lags into the classical SARIMA model improves forecast accuracy. Similar findings have been reported in studies for other indicators, with reductions in MAPE ranging from 0.06 to 3.3 percentage points. These results confirm the potential of using online user activity to enhance the accuracy of forecasts for a variety of indicators.

A comparative analysis of the effectiveness of including search queries in SARIMA forecast models across different economic and demographic topics is presented in Table 5.

In this study, the inclusion of search queries improved forecast accuracy: MAPE decreased from 4.2% to 2.96%, and MAE from 4,320.9 to 3,055.2. These differences were statistically significant according to the Diebold – Mariano test.

A subset of search queries was selected using PCA for specific topics related to reproductive behavior: “Pregnancy Planning,” “Pregnancy Progress,” “Preparing for Childbirth,” and “General Queries.” The study analyzed and compared information criteria for several models that included the resulting principal components either collectively or separately, with various lags. The lag depth was initially determined based on the cross-correlation function and the statistical significance of the corresponding coefficients in the estimated forecasting model.

The best 1-year forecast was achieved by the model including the “Preparing for Childbirth” principal components along with their associated lags.