PhD student Runze Yang has been awarded the Vice-Chancellor’s Commendation for his PhD thesis at Macquarie University.

Thesis title: Deep Fourier-based Time Series Modeling

Thesis abstract:
Time series modeling plays a crucial role in a wide range of real-world applications. Classical time series modeling relies on assumptions of linearity and stationarity, uses handcrafted features, captures only short-term dependencies, and models weak interactions among variables, which limits its ability to describe real-world phenomena. In recent years, deep learning has demonstrated promising performance in time series modeling, including time series forecasting (TSF) and time series classification (TSC). Thus, the deep time series modeling thrive to handle nonlinearity and non-stationarity, automatically learns deep representations, captures long-term dependencies, and models
complex interactions among variables. The Fourier transform is a powerful tool for capturing global periodic patterns, decomposing hierarchical effects, and detecting noise in time series analysis. Motivated by these advances, this thesis aims to develop novel deep learning methods for time series modeling by integrating frequency-domain analysis tools to address emerging research challenges.

This thesis covers five main topics: time–frequency features extraction, time–frequency mapping, interpretable Fourier decomposition, the inclusion of timestamp information, and adaptation to data characteristics. Thus, we identify the following research gaps and summarize our contributions and significance for five topics, respectively: (i) Existing Fourier-based methods for TSF suffer from inconsistent starting cycles and inconsistent series lengths issue, and fail to incorporate time- and frequency-domain features simultaneously. Thus, we propose a Fourier basis expansion to extract time-frequency features, which is grounded in Fourier theory based on basis functions. It can significantly improve the performance of existing TSF backbones by bridging both time and frequency modalities. (ii) There is a lack of effective backbone architectures to map time-frequency features in TSF. Existing TSF methods perform mapping either in the time or frequency domain, and overlook the separation of endogenous and exogenous effects. Therefore, we propose a synergetic time-frequency feature to separate the mapping into trend, seasonal, and interaction components in a time-frequency specialized manner. It can achieve strong TSF performance in both long-term and short-term forecasting tasks. (iii) There is a lack of interpretable frequency-based methods for decomposing various effects in TSF. Existing methods mainly leverage smoothing-based temporal techniques, rather than providing an interpretable, generalizable, and efficient decomposition that is explainable in both the time and frequency domains. Hence, we propose MLOW, an interpretable multi-effect low-rank frequency magnitude decomposition method. MLOW apply low-rank algorithms to the frequency magnitude spectrum to preserve and disentangle the dominant time series effects. It can improve any time-based TSF backbone with substantial performance improvement but minimal architectural modifications. (iv) Existing methods are ineffective in leveraging timestamp information and handling noise in frequency-based TSF models. They fail to extract interpretable and effective information from timestamps. Thus, we propose VH-NBEATS, a variational hierarchical N-BEATS model that handles forecasting based on timestamp, polynomial, and Fourier bases with a variational learning architecture. It provides interpretable TSF forecasting results for timestamps and can be applied to any backbone for better performance. (v) Existing methods do not effectively address data characteristic issues in TSC, such as handling heterogeneous data with different sampling granularities and non-IID distributions. Therefore, we propose BLNet, which addresses data granularity issues using a two-channel architecture for short-time Fourier transform and wavelet transform inputs, along with a blocking variable and data augmentation techniques for non-IID and imbalanced data.