A male amateur distance runner volunteered to participate in the current study. The male runner (aged 44 years, height=169.5 cm, weight=63.8 kg), who is a member of a local distance running club in southern Taiwan, has been participating in regular distance running for >5 years with a training frequency of 3 to 5 times per week and a running distance of >50 km per week. The runner’s personal best in a marathon is 3 hours and 4 minutes. To collect whole-day HR data, the participant was requested to wear a smartwatch (Forerunner 935, Garmin Ltd) throughout the experimental period, except during bathing and/or battery recharging. HR data were acquired via the smartwatch’s photoplethysmography sensor over 24 months.

The data acquisition period spanned from July 2, 2019, to July 1, 2021 (731 days in total), and the personal smartwatch data were collected and synchronized to cloud storage via a commercial app (Garmin Connect Mobile, Garmin Ltd). Through the Garmin Health API, we further synchronized the personal data to our online database built with phpMyAdmin. According to the participant’s Garmin Connect Mobile record, 666 days were recorded as observation days. After consulting with the participant, the 65 missing observation days were mainly due to the participant not wearing the smartwatch for an entire day.

The device-generated default parameters included in the current study were whole-day HR and whole-day steps, which are automatically sampled every 15 seconds. By combining raw daily HR and step data, HR can be categorized into 2 distinct states: sleeping HR and active (nonsleeping) HR. We further calculated average sleep HR, minimum sleeping HR, maximum sleeping HR, active HR, minimum active HR, and maximum active HR (refer to operational definitions in Table 1). Because amateur athletes tend to train more on the weekends [38], Saturday and Sunday were designated as holidays and categorized as exogenous features in the present study. The operational definitions of each parameter are listed in Table 1. For the SARIMA model used in the current study, RHR was the only endogenous feature, while the remaining HR variables and the daily step count were exogenous features (Table 1). The periods for all parameters are shown in Figure 1. The workflow of the model operation is shown in Figure 2.

The parameters belonging to “Today” and “Yesterday” were used for training various models with the goal of predicting the RHR of the “Next day.”

As time progresses, previously accumulated data are continuously incorporated into the training dataset, enabling the recursive execution of predictions to reflect the most up-to-date information and maintain model accuracy over time.

To prevent data leakage, the first 75% of the chronological timeline was used as the training set for initial model estimation, with the remaining 25% serving as the holdout testing set for rolling forecast evaluation.

Raw data generated by smartwatches occasionally contain sensor artifacts or periods of nonwear. In the 666 observed days of this study, physiological readings of 0, which were mainly due to nonwear during the sleep period or a daytime gap in HR tracking, were identified as measurement anomalies and targeted for removal. Specifically, zero values were detected in the main features (RHR; n=14), active HR (n=30), and daily step count (n=1). Because several of these anomalies occurred concurrently on the same calendar day, a total of 42 daily observations were further removed from the 666 observed days. After these anomalous records were removed, the final cleaned dataset for modeling comprised 624 valid daily observations over the 24-month period.

A common challenge in preprocessing wearable data is handling the subsequent chronological gaps caused by these removals. To preserve the integrity of biological data, we explicitly chose not to synthesize or impute missing physiological data (eg, via linear interpolation or mean substitution), as mathematically inventing values during nonwear periods risks introducing artificial trends. Thus, these short chronological gaps were left unaltered. The sktime 0.40.1 (a Python library; Python Software Foundation 3.10.14) algorithmic architecture dynamically accommodates these naturally occurring missing intervals during forecasting, ensuring that the model trains exclusively on authentic physiological measurements.

The study was approved by the National Cheng Kung University Institutional Review Board (A-ER-106-493), and all procedures were conducted in accordance with the ethical standards of the Declaration of Helsinki. The participant signed a written informed consent form and agreed to wear a smartwatch (Forerunner 935) throughout the experimental period. The participant was informed that participation was voluntary and that he had the right to withdraw at any time. All data generated by the smartwatch, including HR metrics synchronized from the Garmin Health database, were deidentified to ensure participant confidentiality. Upon completion of the data acquisition period, the participant was provided with the smartwatch as compensation for his involvement in this case study.

In Table 2, descriptive statistics for each parameter are listed. During the observation period, the distance runner demonstrated a typical pattern of RHR (mean 49.099, SD 2.392 bpm) and sleeping HR (mean 50.952, SD 2.495 bpm). The average daily steps (mean 19,680, SD 10,277 steps/day) also indicated a regular exercise training behavior in the current participant.

In phase 1, five models were trained with the chronologically split dataset (75% training and 25% testing). To establish a comparative baseline, a naive forecaster (which predicted the next day’s RHR as the current day’s RHR) was implemented, yielding an MAE of 2.404 bpm. The remaining 4 models used a SARIMA framework, evaluating 1-day and 7-day rolling forecasting horizons, both with and without exogenous features.

The model performance metrics and automatically selected hyperparameter orders are detailed in Table 3. The models trained with exogenous features demonstrated significantly higher predictive accuracy (Figures 4A and B). The optimal configuration was the 1-day rolling forecast with features, which achieved an MAE of 1.712 bpm and an RMSE of 2.315 bpm, representing a nearly 30% error reduction compared to the naive baseline. The automated hyperparameter selection for this optimal model (Table 3) revealed an ARIMA(0,0,0)(2,0,0)₇ structure; the exogenous features successfully explained day-to-day variance (Table 4), while the seasonal autoregressive terms captured the athlete’s weekly training cycle.

Conversely, models trained without features were relatively less effective in predicting the upcoming daily RHR. In addition to the relatively higher MAE of the nonfeature models (Table 3), the statistical variance metrics (Table 4) and graphs (Figures 4C and D) also showed that the nonfeature models underfit the data.

To isolate the predictive value of individual features used in the optimal phase 1 model, a LOFO ablation analysis was conducted (Table 5). As RHR is a highly stable metric (typically fluctuating only 1-3 bpm daily), absolute error boundaries are inherently tight. However, the ablation revealed significant relative impacts. Omission of the previous day’s RHR was the primary driver of predictive degradation, resulting in a 7.5% relative increase in the MAPE (rising from 3.45% to 3.71%) and an MAE increase of 0.13 bpm. The trimmed mean active HR also contributed positively to the forecast.

Conversely, the simultaneous inclusion of the remaining 10 aggregated metrics (such as sleep HR and step count) exhibited a decrease in error when these features were removed. This confirms that highly complex, multivariable feature sets introduce multicollinearity and mild overfitting when predicting stable physiological baselines. Consequently, to maximize computational efficiency without sacrificing accuracy, a lean 2-feature (ie, RHR and trimmed average active HR) framework was implemented in the phase 3 simulation.

According to the ablation analyses, a feature set consisting exclusively of RHR and trimmed average active HR was established. A new 1-day rolling SARIMA model was established using only the first 21 days of the dataset. Over the subsequent 603-day period, this continuously updating model achieved an MAE of 1.63 bpm and an RMSE of 2.16 bpm (Table 6). As detailed in Table 6, this short-initiation model demonstrated comparable performance across the testing period.

In the present study, continuous time-series HR data from a commercial wearable device were used to forecast the next-day (1-day rolling forecast) or next-week (7-day rolling forecast) RHR for a distance runner. Within the scope of this case study, a 3-phase evaluation indicated that multivariate SARIMA models performed better than univariate approaches and naive baselines. These results suggest that predicted RHR derived from prior HR parameters may serve as a readiness reference for upcoming exercise training.

In the current study, our phase 2 ablation analysis revealed that combining RHR with exogenous features improved accuracy. Conversely, including all features led to multicollinearity and mild overfitting. As the current study aimed to develop a prediction tool to support a healthy adult distance runner, exercise training was expected to be the primary contributor to fluctuations in daily HR data, as different levels of exercise training exert distinct influences on autonomic modulation, HR indices, and HRV [39-41]. In this case, using HR-derived features as data sources was streamlined and sufficient to create a statistically useful model. In the current study, we found that both 1-day and 7-day SARIMA models with exogenous features could generate RHR predictions that can be used to inform sports training practice. The 1-day model can serve a precautionary function, allowing the athlete to adjust training, while the 7-day RHR prediction can forecast readiness over the next week, helping the athlete plan the upcoming microcycle training schedule.

However, the current study shows that the true day-to-day RHR fluctuations of the runner ranged from 0 to 10 (bpm), whereas the 1-day and 7-day SARIMA models with exogenous features showed predicted RHR changes of only 0 to 4 (bpm) across calendar days. Theoretically, HR is easily affected by various internal or external environments [32]. A forthcoming full-day RHR is sensitive to various stressors [42-45] (eg, life events, diet, and clinical symptoms) that occur randomly and are currently out of scope for these exogenous feature-included SARIMA models. Some of these stressors can have longer-term effects on the next-day or next-week HR, such as influenza or seasonal allergies [44,46], while some are temporary, such as dehydration or caffeine intake, which can cause a heart rate shift [47,48]. In contrast to clinical symptoms, random stressors might merely induce a diurnal HR shift rather than serve as determining factors for the subsequent day’s HR. In other words, these factors are transient stressors that leave no residual effects for the next day. Taken together, the predictive capacity of the current exogenous feature-included SARIMA models may be compromised because they do not include other effective stressors beyond exercise training.

Nevertheless, this case study established a streamlined model for predicting future RHR that is applicable to exercise training practices. To develop a more accurate predictive model, additional endogenous or exogenous features need to be included and investigated.

Technically, HRV indices, which are affected by the autonomic nervous system, can be used to indicate or evaluate the status of overtraining [49,50]. There are multiple HRV indices representing sympathetic and parasympathetic nerve activity, such as RR intervals plotted against time, the RR intervals’ standard deviation (SDNN), the root mean square successive difference (rMSSD), and the amount of neighboring RR intervals varying >50 milliseconds expressed in percentage (pNN50). However, despite their academic value, HRV analysis outputs are neither intuitive nor user-friendly. Moreover, the validity of HRV analyses is relatively sensor-dependent. In reality, comparing HRV measurements from commercial wearable devices indicates that the overall validity is currently poor under free-living conditions [51]. Therefore, using RHR is preferred as an indicator of long-term monitoring of training or physiological status due to its relative feasibility and reliability.

A primary limitation of statistical time-series forecasting in this context is its tendency to smooth extreme daily fluctuations, which likely accounts for the lower prediction variance observed relative to the ground-truth data. To better capture these sharp RHR dynamics, future studies should incorporate additional internal and external stressors as feature inputs and explore machine learning or deep learning architectures beyond traditional statistical models.

Additionally, missing data due to nonwear or improper device placement may pose a practical challenge for continuous RHR forecasting. Under the current ARIMA model, if yesterday’s data are unavailable, feature data from 2 days prior are substituted to predict today’s RHR. Within the phase 3 testing set, the MAE values for predicted RHR, with and without yesterday’s data feature, were 1.637 and 1.517 bpm, respectively. This indicates that nonequidistant sampling did not compromise forecast performance in this case report. However, because the participant of the current study demonstrated high compliance and maintained a consistent training schedule, his relatively stable physiological baseline may have mitigated the impact of missing data. In broader real-world applications, nonwear intervals may need to be modeled as an exogenous feature to account for underlying physiological shifts associated with life event–related disruptions, such as sudden illness or prolonged sedentary periods.

Predicting an athlete’s next-day physiological recovery metrics, such as RHR and HRV, is an evolving area in sports science and predictive analytics. As previously noted, existing literature using classical time-series modeling is limited; for instance, only one study has used an ARIMA model to predict the next 1-hour HR in healthy young male individuals from a 24-hour database [36]. In addition, a recent study demonstrated that machine learning approaches (ie, support vector regression [SVR] and Extreme Gradient Boosting [XGBoost]) could predict next-day HRV by using external training loads (total mechanical work in kilojoules) and internal training loads (rate of perceived exertion) as primary feature sources [52], which is somewhat complicated and dependent on multiple sensors. Thus, extending the forecasting horizon to predict next-day HR would provide a more intuitive and practically applicable framework for managing athletic training. In phase 3 of our analysis, we tested the potential commercial applicability of the current models. In contrast to the >400-day model training, phase 3 adopted a short-initiation model that included only a 21-day training period with 2 features (ie, RHR and the trimmed average active HR). The comparable outcomes between the full-history and short-initiation models suggest that a 3-week period of model training may be sufficient to establish a mathematical RHR predictive function applicable to exercise training practice.

As HR is a straightforward index readily available from commercial devices, predicted RHR can be used as an indicator of future physiological status. According to the present study’s findings, 1-day or 7-day RHR forecasts can serve as a reference for short-term adjustments or longer-term planning for upcoming training. It would be worthwhile to further apply this methodology to various issues in endurance training. In addition, as an abnormally raised RHR is also an indicator of up-regulated sympathetic activity [53], future RHR forecasts can be a health security solution to protect people from extremely high stress.

In conclusion, using longitudinal HR measurements, we developed a statistical time-series framework for predicting the next-day and next-week RHR of a distance runner. By isolating the most predictive features, we demonstrated that 3 weeks of data can initiate a lean, continuously updating SARIMA model that achieves performance comparable to that of the full-history model. Further studies that include more exogenous features and a larger number of participants are needed to verify the framework’s applicability.