Trend filtering simplifies complex time series data by applying smoothness to
filter out noise while emphasizing proximity to the original data. However,
existing trend filtering methods fail to reflect abrupt changes in the trend
due to `approximateness,' resulting in constant smoothness. This
approximateness uniformly filters out the tail distribution of time series
data, characterized by extreme values, including both abrupt changes and noise.
In this paper, we propose Trend Point Detection formulated as a Markov Decision
Process (MDP), a novel approach to identifying essential points that should be
reflected in the trend, departing from approximations. We term these essential
points as Dynamic Trend Points (DTPs) and extract trends by interpolating them.
To identify DTPs, we utilize Reinforcement Learning (RL) within a discrete
action space and a forecasting sum-of-squares loss function as a reward,
referred to as the Dynamic Trend Filtering network (DTF-net). DTF-net
integrates flexible noise filtering, preserving critical original subsequences
while removing noise as required for other subsequences. We demonstrate that
DTF-net excels at capturing abrupt changes compared to other trend filtering
algorithms and enhances forecasting performance, as abrupt changes are
predicted rather than smoothed out.

提出了一种基于马尔可夫决策过程 (Markov Decision Process, MDP) 的趋势点检测方法，利用强化学习在离散动作空间中进行，通过预测平方损失函数作为奖励来提取动态趋势点 (Dynamic Trend Points, DTPs)，以此纠正因 ' 近似性 ' 而导致的平滑趋势，并在同时去除噪声的过程中保留重要的原始子序列，从而增强预测性能。