Multivariate time series forecasting with hierarchical structure is widely used in real-world applications, e.g., sales predictions for the geographical hierarchy formed by cities, states, and countries. The hierarchical time series (HTS) forecasting includes two sub-tasks, i.e., forecasting and reconciliation. In the previous works, hierarchical information is only integrated in the reconciliation step to maintain coherency, but not in forecasting step for accuracy improvement. In this paper, we propose two novel tree-based feature integration mechanisms, i.e., top-down convolution and bottom-up attention to leverage the information of the hierarchical structure to improve the forecasting performance. Moreover, unlike most previous reconciliation methods which either rely on strong assumptions or focus on coherent constraints only, we utilize deep neural optimization networks, which not only achieve coherency without any assumptions, but also allow more flexible and realistic constraints to achieve task-based targets, e.g., lower under-estimation penalty and meaningful decision-making loss to facilitate the subsequent downstream tasks. Experiments on real-world datasets demonstrate that our tree-based feature integration mechanism achieves superior performances on hierarchical forecasting tasks compared to the state-of-the-art methods, and our neural optimization networks can be applied to real-world tasks effectively without any additional effort under coherence and task-based constraints.

State space model (SSM) provides a general and flexible forecasting framework for time series. Conventional SSM with fixed-order Markovian assumption often falls short in handling the long-range temporal dependencies and/or highly non-linear correlation in time-series data, which is crucial for accurate forecasting. To this extend, we present External Memory Augmented State Space Model (EMSSM) within the sequential Monte Carlo (SMC) framework. Unlike the common fixed-order Markovian SSM, our model features an external memory system, in which we store informative latent state experience, whereby to create ``memoryful" latent dynamics modeling complex long-term dependencies. Moreover, conditional normalizing flows are incorporated in our emission model, enabling the adaptation to a broad class of underlying data distributions. We further propose a Monte Carlo Objective that employs an efficient variational proposal distribution, which fuses the filtering and the dynamic prior information, to approximate the posterior state with proper particles. Our results demonstrate the competitiveness of forecasting performance of our proposed model comparing with other state-of-the-art SSMs.