TILDE-Q: A Transformation Invariant Loss Function for Time-Series Forecasting

Time-series forecasting has gained increasing attention in the field of artificial intelligence due to its potential to address real-world problems across various domains, including energy, weather, traffic, and economy. While time-series forecasting is a well-researched field, predicting complex temporal patterns such as sudden changes in sequential data still poses a challenge with current models. This difficulty stems from minimizing Lp norm distances as loss functions, such as mean absolute error (MAE) or mean square error (MSE), which are susceptible to both intricate temporal dynamics modeling and signal shape capturing. Furthermore, these functions often cause models to behave aberrantly and generate uncorrelated results with the original time-series. Consequently, developing a shape-aware loss function that goes beyond mere point-wise comparison is essential. In this paper, we examine the definition of shape and distortions, which are crucial for shape-awareness in time-series forecasting, and provide a design rationale for the shape-aware loss function. Based on our design rationale, we propose a novel, compact loss function called TILDEQ (Transformation Invariant Loss function with Distance EQuilibrium) that considers not only amplitude and phase distortions but also allows models to capture the shape of time-series sequences. Furthermore, TILDE-Q supports the simultaneous modeling of periodic and nonperiodic temporal dynamics. We evaluate the efficacy of TILDE-Q by conducting extensive experiments under both periodic and nonperiodic conditions with various models ranging from naive to state-of-the-art. The experimental results show that the models trained with TILDE-Q surpass those trained with other metrics, such as MSE and DILATE, in various real-world applications, including electricity, traffic, illness, economics, weather, and electricity transformer temperature (ETT).