Google Trends 与 COVID-19 时序预测研究提出 DPRS 方向性预测强度指标
Asymmetric Bidirectional Predictive Dynamics in Google Search and COVID-19 Time Series: A Multi-Horizon Forecast-Error Analysis
用 LightGBM 对 Google Trends 和疫情数据做双向预测分析，还提出了 DPRS 这个新指标，做时序预测的可以看看误差分布熵的思路。
研究以 8 组预设的 Google Trends 与 COVID-19 数据配对为对象，用 LightGBM 在 400 天滚动窗口、1-14 天预测期上做双向匹配预测。论文引入 FEDE（预测误差分布熵）和 0-100 分制的 DPRS 方向性预测响应强度指标。结果显示"loss of smell"到确诊病例方向以精度为主，平均 log-RMSE 增益 0.104（约 9.9% 的 RMSE 等效下降），DPRS 达 100；而"covid test"到阳性率方向虽 RMSE 增益为负，却呈 FEDE 主导（D_FEDE=0.039，72% 窗口为正），DPRS 为 98。结论指出预测精度与误差分布动态互补，预测效应依赖方向和指标，聚合模式不能外推到单个时间点或作为因果证据。
Asymmetric Bidirectional Predictive Dynamics in Google Search and COVID-19 Time Series: A Multi-Horizon Forecast-Error Analysis
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.