In this thesis, we explore novel approaches to time series forecasting across several domains. Our first direction of research involves the forecasting of network time series models. We propose an extension of generalised network autoregressive (GNAR) models to include exogenous variables (GNARX). We then demonstrate the superior forecasting performance of GNARX models compared to traditional vector autoregressive models when assessing the impact of the COVID-19 pandemic on global business confidence, exploiting the information contained in trade network data and exogenous public health policy variables.

Our next contribution is to develop a novel class of models for mixed frequency data analysis, Fully NonParametric MIDAS (FNP-MIDAS). This extends the MIxed DAta Sampling (MIDAS) framework by incorporating nonlinear component functions, offering a more flexible handling of temporal dependencies and lags. We develop a backfitting estimation algorithm and apply the recently-developed trend filtering nonparametric regression method, showing that FNP-MIDAS exhibits significant improvements in forecasting urban atmospheric pollution levels over its linear counterparts.

We then dive into the realm of feature engineering, examining the utility of non-decimated wavelet features and non-decimated wavelet packet features for a wide range of forecasting applications. Our investigation encompasses both temporal and non-temporal machine learning methods, and both one-step-forward predictions and long-horizon forecasts. We find sizable benefits to using wavelet features rather than lagged features for the vast majority of experimental cases.

Lastly, we present the Neural Factor Model, a novel feedforward neural network architecture for forecasting large cap global stock returns using a high dimensional dataset. By integrating factor characteristics, cross-asset returns, and macroeconomic data within a hierarchical structure together with various parameter constraints, this model minimizes overfitting risks and showcases strong backtest performance for a hypothetical long-short investment strategy.