Multi-step ahead forecasting is still an open challenge in time series forecasting. Several approaches that deal with this complex problem have been proposed in the literature but an extensive comparison on a large number of tasks is still missing. This paper aims to fill this gap by reviewing existing strategies for multi-step ahead forecasting and comparing them in theoretical and practical terms. To attain such an objective, we performed a large scale comparison of these different strategies using a large experimental benchmark (namely the 111 series from the NN5 forecasting competition). In addition, we considered the effects of deseasonalization, input variable selection, and forecast combination on these strategies and on multi-step ahead forecasting at large. The following three findings appear to be consistently supported by the experimental results: Multiple-Output strategies are the best performing approaches, deseasonalization leads to uniformly improved forecast accuracy, and input selection is more effective when performed in conjunction with deseasonalization.

A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition

The increasing availability of large amounts of historical data and the need of performing accurate forecasting of future behavior in several scientific and applied domains demands the definition of robust and efficient techniques able to infer from observations the stochastic dependency between past and future. The forecasting domain has been influenced, from the 1960s on, by linear statistical methods such as ARIMA models. More recently, machine learning models have drawn attention and have established themselves as serious contenders to classical statistical models in the forecasting community. This chapter presents an overview of machine learning techniques in time series forecasting by focusing on three aspects: the formalization of one-step forecasting problems as supervised learning tasks, the discussion of local learning techniques as an effective tool for dealing with temporal data and the role of the forecasting strategy when we move from one-step to multiple-step forecasting.

Machine Learning Strategies for Time Series Forecasting

This article presents a comparison of forecasting performance for a variety of linear and nonlinear time series models using the U.S. unemployment rate. Our main emphases are on measuring forecasting performance during economic expansions and contractions by exploiting the asymmetric cyclical behavior of unemployment numbers, on building vector models that incorporate initial jobless claims as a leading indicator, and on utilizing additional information provided by the monthly rate for forecasting the quarterly rate. Comparisons are also made with the consensus forecasts from the Survey of Professional Forecasters. In addition, the forecasts of nonlinear models are combined with the consensus forecasts. The results show that significant improvements in forecasting accuracy can be obtained over existing methods.

Forecasting the U.S. Unemployment Rate

It is shown how Markov chain theory can be exploited to study non-linear time series, the emphasis being on the classification into stationary and non-stationary models. A generalized h-step version of the Tweedie (1975), (1976) criteria is formulated, and applications are given to a number of non-linear models. New results are obtained, and known results are shown to emerge as special cases in both the scalar and vector case. A connection to stability theory is briefly discussed, and it is indicated how the Markov property can be utilized for estimation purposes.

Non-linear time series and markov chains

The impact of energy consumption on economic growth: Evidence from linear and nonlinear models in Taiwan

Threshold models for nonlinear time series analysis.

Building stocks in cities have consumed a large amount of energy and resources globally, resulting in serious greenhouse gas pollution and environmental problems. As a circular economy has become one of the effective solutions to current environmental problems, energy and material circularity indicators of building stocks in cities become important instruments for city planners in creating sustainable and resilient cities. However, such evaluation requires a high level of integration of both spatial and attribute information of both buildings and cities. A highly integrated system is required to produce reliable analysis results. This study aims to create an evaluation tool for city planners through utilizing information contained via Building Information Modeling and Geographic Information System. Through this tool, planners and decision makers can understand current and future circularity and environmental impacts of building stocks in cities and therefore can propose the most suitable planning and governance strategies and policies. Through visualization of simulation results on an information platform, the awareness of a circular city could also be raised. Taipei city and its city master plan are used as a case study for validation of the proposed tool.

S. H. Hsieh

Papers

Threshold models for nonlinear time series analysis.

Combining BIM & GIS Information to Simulate Circularity of Building Stocks in a City—A Case Study of Taipei City