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Asymmetric Bidirectional Predictive Dynamics in Google Search and COVID-19 Time Series: A Multi-Horizon Forecast-Error Analysis

Andrei Velichko, Imen Mahmoud · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28563 · cited by 0 works (OpenAlex) · open-access PDF

Portuguese

A atividade de busca de pontos de bloqueio on-line é amplamente utilizada como um rastro digital de informações procuradas durante as epidemias, mas seu valor preditivo é frequentemente reduzido a correlação, um atraso de direção selecionado ou uma pontuação de erro de previsão única. Nós examinamos oito pares de Google Trends-COVID-19 pré-determinados em ambas as direções usando previsões LightGBM correspondentes sobre janelas de rodagem de 400 dias e horizontes de 1-14 dias. O ganho de Log-RMSE é combinado com a entropia de distribuição de erro de previsão-direção única (FEDE), que captura mudanças positivas, dependentes do horizonte, positivas na distribuição de erro assinada. A força de resposta preditiva concisa concisa extra persistente (PRD

Machine translation (Meta M2M100); the English original follows.

Abstract

Online search activity is widely used as a digital trace of information seeking during epidemics, but its predictive value is often reduced to correlation, a selected lag, or a single forecast-error score. We examine eight pre-specified Google Trends-COVID-19 pairs in both directions using matched LightGBM forecasts over rolling 400-day windows and horizons of 1-14 days. Log-RMSE gain is combined with forecast-error distribution entropy (FEDE), which captures horizon-dependent changes in the signed error distribution. The resulting directional predictive signature comprises response class, RMSE effect, FEDE endpoint and early-slope responses, persistence across rolling regimes, and horizon profile. For screening candidate directions, we also introduce a relative persistence-weighted directional predictive response strength (DPRS) on a within-study 0-100 scale; 100 denotes the strongest observed response in the comparison set, not an absolute coupling maximum. The pairs show concordant, RMSE-only, FEDE-only, and mixed responses. "loss of smell" -> reported cases is accuracy-dominant, with mean log-RMSE gain 0.104 (about 9.9% equivalent RMSE reduction) and DPRS 100, whereas the reverse direction is FEDE-dominant (D_FEDE=0.048; DPRS=42). "covid test" -> positive rate is FEDE-dominant (D_FEDE=0.039; positive in 72% of windows; DPRS=98) despite negative RMSE gain, while "lockdown" -> stringency is the clearest concordant case (DPRS=78). World-level symptom/case pairs are less persistent. Thus, forecast accuracy and error-distribution dynamics are complementary, predictive effects can be direction- and metric-dependent, and forecast horizon is part of the relationship. Aggregated regime-level patterns should not be extrapolated to individual time points or interpreted as evidence of causality.

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Topics: Mean squared error, Mathematics, Statistics, Predictive value, Mean squared prediction error, Entropy (arrow of time)

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