Accurate time series forecasting underpins decision-making across domains, yet conventional ML development suffers from data scarcity in new deployments, poor adaptability under distribution shift, and diminishing returns from manual iteration. We propose Self-Evolving Agent for Time Series Algorithms (SEA-TS), a framework that autonomously generates, validates, and optimizes forecasting code via an iterative self-evolution loop. Our framework introduces three key innovations: (1) Metric-Advantage Monte Carlo Tree Search (MA-MCTS), which replaces fixed rewards with a normalized advantage score for discriminative search guidance; (2) Code Review with running prompt refinement, where each executed solution undergoes automated review followed by prompt updates that encode corrective patterns, preventing recurrence of similar errors; and (3) Global Steerable Reasoning, which compares each node against global best and worst solutions, enabling cross-trajectory knowledge transfer. We adopt a MAP-Elites archive for architectural diversity. On the public Solar-Energy benchmark, SEA-TS generated code achieves a 40% MAE reduction relative to TimeMixer, surpassing state-of-the-art methods. On proprietary datasets, SEA-TS generated code reduces WAPE by 8.6% on solar PV forecasting and 7.7% on residential load forecasting compared to human-engineered baselines, and achieves 26.17% MAPE on load forecasting versus 29.34% by TimeMixer. Notably, the evolved models discover novel architectural patterns--including physics-informed monotonic decay heads encoding solar irradiance constraints, per-station learned diurnal cycle profiles, and learnable hourly bias correction--demonstrating that autonomous ML engineering can generate genuinely novel algorithmic ideas beyond manual design.