Time series modelling and forecasting is a persistent problem with extensive implications in scientific, business, industrial, and economic areas. This thesis’ contribution is twofold. Firstly, we propose a novel probabilistic time series forecasting methodology that introduces the use of Fourier domain-based attention models. We denote Spectral Attention (SA) to this frequency domain-based attention mechanism, which merges classic signal processing spectral filtering techniques with machine learning architectures. Secondly, in the context of high-frequency trading, we take advantage of the abundance of intraday financial data to develop deep learning-based solutions for modelling financial time series. Machine learning methods can potentially enhance the performance of traditional methodologies used by practitioners. Deep neural networks’ feature extraction capabilities, which can benefit from the rising accessibility of high-frequency data, and attention mechanisms, which help to model temporal patterns, are mostly to blame for this.

Concerning our first major contribution, this thesis demonstrates that spectral domain-based machine learning models can learn the properties of time series datasets and integrate this information to improve forecasting accuracy. Simultaneously, Fourier domain-based models alleviate some of the inconveniences commonly associated with deep autoregressive models. These architectures, prone to prioritising recent past data, often ignore critical global information not contained in previous time steps. Additionally, they are susceptible to error accumulation and propagation and may not yield explainable results. The proposed model, the Spectral Attention Autoregressive Model (SAAM), mitigates these problems by combining deep autoregressive models with a Spectral Attention (SA) module. This module uses two attention models operating over the Fourier domain representation of the time series’ embedding. Through spectral filtering, SAAM differentiates between the components of the frequency domain that should be considered noise and subsequently filtered out, and the global patterns that are relevant and should be incorporated into the predictions. We prove how the proposed Spectral Attention module can be integrated into most deep autoregressive models, consistently improving the results of these base architectures and achieving state-of-the-art performance. Our contribution’s modularity offers significant opportunities for performance improvement in the literature on time series modelling and forecasting.

Afterwards, this thesis shifts toward showcasing the benefits of machine learning solutions in two different quantitative finance scenarios, proving how attention-based deep learning approaches compare favourably to classic parametric-based models and providing solutions for various algorithmic and high-frequency trading problems.

In the context of volatility forecasting, which plays a central role among equity risk measures,  we show that Dilated Causal Convolutional-based neural networks offer significant performance gains compared to well-established volatility-oriented parametric models. The proposed model, called DeepVol,  showcases how data-driven models can avoid the limitations of classical methods by taking advantage of the abundance of high-frequency data. DeepVol outperforms baseline methods while exhibiting robustness in the presence of volatility shocks, showing its ability to extract universal features and transfer learning to out-of-distribution data. Consequently, data-driven approaches should be carefully considered in the context of volatility forecasting, as they can be instrumental in the valuation of financial derivatives, risk management, and the formation of investment portfolios.

Finally, this thesis presents a survival analysis model for estimating the distribution of fill times for limit orders posted in the Limit Order Book (LOB). The proposed model, which does not make assumptions about the underlying stochastic processes, employs a convolutional-Transformer encoder and a monotonic neural network decoder to relate the time-varying features of the LOB to the distribution of fill times. It grants practitioners the capability of making informed decisions between market orders and limit orders, which in practice entails a trade-off between immediate execution and price premium. We offer an exhaustive comparison of the survival functions resulting from different order placement strategies, offering insight into the fill probability of orders placed within the spread. Empirical evaluation reveals the superior performance of the monotonic encoder-decoder convolutional-Transformer compared to state-of-the-art benchmarks, leading to more accurate predictions and improved economic value.