A bias and variance analysis for multistep-ahead time series forecasting

Souhaib Ben Taieb, Amir F. Atiya

Research output: Contribution to journalArticleResearchpeer-review

122 Citations (Scopus)


Multistep-ahead forecasts can either be produced recursively by iterating a one-step-ahead time series model or directly by estimating a separate model for each forecast horizon. In addition, there are other strategies; some of them combine aspects of both aforementioned concepts. In this paper, we present a comprehensive investigation into the bias and variance behavior of multistep-ahead forecasting strategies. We provide a detailed review of the different multistep-ahead strategies. Subsequently, we perform a theoretical study that derives the bias and variance for a number of forecasting strategies. Finally, we conduct a Monte Carlo experimental study that compares and evaluates the bias and variance performance of the different strategies. From the theoretical and the simulation studies, we analyze the effect of different factors, such as the forecast horizon and the time series length, on the bias and variance components, and on the different multistep-ahead strategies. Several lessons are learned, and recommendations are given concerning the advantages, disadvantages, and best conditions of use of each strategy.
Original languageEnglish
Article number7064712
Pages (from-to)62-76
Number of pages15
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number1
Publication statusPublished - 1 Jan 2016
Externally publishedYes


  • Bias
  • machine learning
  • Monte Carlo simulation
  • multistep-ahead forecasting
  • nearest neighbors
  • neural networks (NNs)
  • time series
  • variance

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