Encoding Temporal Statistical-space Priors via Augmented Representation

TL;DR

This paper tackles forecasting of complex, non-stationary time series with limited data by introducing Statistical-space Augmented Representation (SSAR). SSAR computes per-time-step statistical measures over a sliding window, converts them into a directed, weighted graph that augments the original time-series inputs, and feeds this non-Euclidean representation into temporal graph learning models such as diffusion t-GCN and t-GCN. The approach is theoretically motivated by a data-generating process with endogenous and exogenous components and is empirically validated on two financial datasets, where SSAR outperforms strong baselines (GRU, LSTM, Linear, NLinear, DLinear) and ablations show robustness and interpretability. The results demonstrate that integrating a statistically-informed prior at each time step improves generalization, stability, and out-of-sample performance in non-stationary, high-noise settings, with broad modularity for different downstream models.

Abstract

Modeling time series data remains a pervasive issue as the temporal dimension is inherent to numerous domains. Despite significant strides in time series forecasting, high noise-to-signal ratio, non-normality, non-stationarity, and lack of data continue challenging practitioners. In response, we leverage a simple representation augmentation technique to overcome these challenges. Our augmented representation acts as a statistical-space prior encoded at each time step. In response, we name our method Statistical-space Augmented Representation (SSAR). The underlying high-dimensional data-generating process inspires our representation augmentation. We rigorously examine the empirical generalization performance on two data sets with two downstream temporal learning algorithms. Our approach significantly beats all five up-to-date baselines. Moreover, the highly modular nature of our approach can easily be applied to various settings. Lastly, fully-fledged theoretical perspectives are available throughout the writing for a clear and rigorous understanding.

Figures (7)

• Figure 1: Sample $\mathcal{G}^t$, $N:=3$
• Figure 2: Real-world causal chains
• Figure 3: Sliding windows
• Figure 4: Data Set 2 results (Box-and-Whisker, MSE)
• Figure 5: Histogram of minimum MSE given $w_s$ (both data sets)

Theorems & Definitions (1)

• Definition 4.1