The weak innovation representation improves forecasting accuracy by providing a more robust and flexible framework for capturing the underlying probability distribution of time series data. Traditional parametric methods, such as ARMA models, often make strong assumptions about the form of the underlying distribution, which can lead to model mismatch and reduced accuracy when faced with highly dynamic and volatile data. In contrast, the weak innovation representation allows for nonparametric modeling of time series data without imposing strict constraints on the distribution.
By using an autoencoder structure that extracts innovations from past observations, WIAE-GPF is able to generate future samples conditioned on these innovations. This approach leverages Bayesian sufficiency, ensuring that decision-making based on these forecasts is optimal without loss in performance. Additionally, by constraining the latent process to be IID uniform through Wasserstein GAN learning, WIAE-GPF produces accurate forecasts that match the true conditional distribution of the forecasted variables.