Batch and incremental dynamic factor machine learning for multivariate and multi-step-ahead forecasting

Robust Multi-Dimensional Time Series Forecasting

Large-scale and high-dimensional time series data are widely generated in modern applications such as intelligent transportation and environmental monitoring. However, such data contains much noise, outliers, and missing values due to interference during measurement or transmission. Directly forecasting such types of data (i.e., anomalous data) can be extremely challenging. The traditional method to deal with anomalies is to cut out the time series with anomalous value entries or replace the data. Both methods may lose important knowledge from the original data. In this paper, we propose a multidimensional time series forecasting framework that can better handle anomalous values: the robust temporal nonnegative matrix factorization forecasting model (RTNMFFM) for multi-dimensional time series. RTNMFFM integrates the autoregressive regularizer into nonnegative matrix factorization (NMF) with the application of the L2,1 norm in NMF. This approach improves robustness and alleviates overfitting compared to standard methods. In addition, to improve the accuracy of model forecasts on severely missing data, we propose a periodic smoothing penalty that keeps the sparse time slices as close as possible to the time slice with high confidence. Finally, we train the model using the alternating gradient descent algorithm. Numerous experiments demonstrate that RTNMFFM provides better robustness and better prediction accuracy.

Machine Learning and Traditional Econometric Models: A Systematic Mapping Study

Context: Machine Learning (ML) is a disruptive concept that has given rise to and generated interest in different applications in many fields of study. The purpose of Machine Learning is to solve real-life problems by automatically learning and improving from experience without being explicitly programmed for a specific problem, but for a generic type of problem. This article approaches the different applications of ML in a series of econometric methods.

Objective: The objective of this research is to identify the latest applications and do a comparative study of the performance of econometric and ML models. The study aimed to find empirical evidence for the performance of ML algorithms being superior to traditional econometric models. The Methodology of systematic mapping of literature has been followed to carry out this research, according to the guidelines established by [39], and [58] that facilitate the identification of studies published about this subject.

Results: The results show, that in most cases ML outperforms econometric models, while in other cases the best performance has been achieved by combining traditional methods and ML applications.

Conclusion: inclusion and exclusions criteria have been applied and 52 articles closely related articles have been reviewed. The conclusion drawn from this research is that it is a field that is growing, which is something that is well known nowadays and that there is no certainty as to the performance of ML being always superior to that of econometric models.

Factor-Based Framework for Multivariate and Multi-step-ahead Forecasting of Large Scale Time Series

State-of-the-art multivariate forecasting methods are restricted to low dimensional tasks, linear dependencies and short horizons. The technological advances (notably the Big data revolution) are instead shifting the focus to problems characterized by a large number of variables, non-linear dependencies and long forecasting horizons. In the last few years, the majority of the best performing techniques for multivariate forecasting have been based on deep-learning models. However, such models are characterized by high requirements in terms of data availability and computational resources and suffer from a lack of interpretability. To cope with the limitations of these methods, we propose an extension to the DFML framework, a hybrid forecasting technique inspired by the Dynamic Factor Model (DFM) approach, a successful forecasting methodology in econometrics. This extension improves the capabilities of the DFM approach, by implementing and assessing both linear and non-linear factor estimation techniques as well as model-driven and data-driven factor forecasting techniques. We assess several method integrations within the DFML, and we show that the proposed technique provides competitive results both in terms of forecasting accuracy and computational efficiency on multiple very large-scale (>10² variables and > 10³ samples) real forecasting tasks.