A Bias and Variance Analysis for Multistep-Ahead Time Series Forecasting

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A Multi-Horizon Quantile Recurrent Forecaster (2017, methodology): “A comprehensive comparison by Taieb and Atiya, 2016 investigated different multi-step strategies with Neural Networks, and recommended the Direct Multi-Horizon strategy: directly train a model with a multivariate target ( y t +1 , · · · , y t + k ) .”
N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting (2022, background): “Conversely, in the joint forecasting strategy, a single model produces fore-casts for all steps in one shot, striking the perfect balance between variance and bias, avoiding error accumulation and leveraging shared model parameters (Bao, Xiong, and Hu 2014; Atiya and Taieb 2016; Wen et al. 2017).”
Predictability of monthly temperature and precipitation using automatic time series forecasting methods (2018, methodology): “Multi-step ahead forecasting has been examined theoretically (e.g. De Gooijer and Klein 1992a, b; Franses and Legerstee 2010; Pemberton 1987; Stoica and Nehorai 1989; Taieb and Atiya 2016; Wei 2006, pp. 88-107) and empirically (Papacharalampous et al. 2017a, c).”
Multi-Horizon Time Series Forecasting with Temporal Attention Learning (2019, background): “Taieb and Atiya [28] analyzed the performance of different multi-horizon forecasting strategies on synthetic datasets with different factors, such as length of time series and number of horizons.”