Time series classification faces two unavoidable problems. One is partial feature information and the other is poor label quality, which may affect model performance. To address the above issues, we create a label correction method to time series data with meta-learning under a multi-task framework. There are three main contributions. First, we train the label correction model with a two-branch neural network for the outer loop. While in the model-agnostic inner loop, we use pre-existing classification models in a multi-task way and jointly update the meta-knowledge, which makes us achieve adaptive labeling on complex time series. Second, we devise new data visualization methods for both image patterns of the historical data and data in the prediction horizon. Finally, we test our method with various financial datasets, including XOM, S\&P500, and SZ50. Results show that our method is more effective and accurate than some existing label correction techniques.

With the fast development of modern deep learning techniques, the study of dynamic systems and neural networks is increasingly benefiting each other in a lot of different ways. Since uncertainties often arise in real world observations, SDEs (stochastic differential equations) come to play an important role. To be more specific, in this paper, we use a collection of SDEs equipped with neural networks to predict long-term trend of noisy time series which has big jump properties and high probability distribution shift. Our contributions are, first, we explored SDEs driven by $\alpha$-stable L\'evy motion to model the time series data and solved the problem through neural network approximation. Second, we theoretically proved the convergence of the model and obtained the convergence rate. Finally, we illustrated our method by applying it to stock marketing time series prediction and found the convergence order of error.