Continuous stress forecasting could potentially contribute to lifestyle interventions. This paper presents a novel, explainable, and individualized approach for stress prediction using physiological data from consumer-grade smartwatches. We develop a time series forecasting model that leverages multivariate features, including heart rate variability, activity patterns, and sleep metrics, to predict stress levels across 16 temporal horizons (History window: 3, 5, 7, 9 days; forecasting window: 1, 3, 5, 7 days). Our evaluation involves 16 participants monitored for 10-15 weeks. We evaluate our approach across 16 participants, comparing against state-of-the-art time series models (Informer, TimesNet, PatchTST) and traditional baselines (CNN, LSTM, CNN-LSTM) across multiple temporal horizons. Our model achieved performance with an MSE of 0.053, MAE of 0.190, and RMSE of 0.226 in optimal settings (5-day input, 1-day prediction). A comparison with the baseline models shows that our model outperforms TimesNet, PatchTST, CNN-LSTM, LSTM, and CNN under all conditions, representing improvements of 36.9%, 25.5%, and 21.5% over the best baseline. According to the explanability analysis, sleep metrics are the most dominant and consistent stress predictors (importance: 1.1, consistency: 0.9-1.0), while activity features exhibit high inter-participant variability (0.1-0.2). Most notably, the model captures individual-specific patterns where identical features can have opposing effects across users, validating its personalization capabilities. These findings establish that consumer wearables, combined with adaptive and interpretable deep learning, can deliver relevant stress assessment adapted to individual physiological responses, providing a foundation for scalable, continuous, explainable mental health monitoring in real-world settings.