Multiple seasonal patterns play a key role in time series forecasting, especially for business time series where seasonal effects are often dramatic. Previous approaches including Fourier decomposition, exponential smoothing, and seasonal autoregressive integrated moving average (SARIMA) models do not reflect the distinct characteristics of each period in seasonal patterns, such as the unique behavior of specific days of the week in business data. We propose a multi-dimensional hierarchical model. Intermediate parameters for each seasonal period are first estimated, and a mixture of intermediate parameters is then taken, resulting in a model that successfully reflects the interactions between multiple seasonal patterns. Although this process reduces the data available for each parameter, a robust estimation can be obtained through a hierarchical Bayesian model implemented in Stan. Through this model, it becomes possible to consider both the characteristics of each seasonal period and the interactions among characteristics from multiple seasonal periods. Our new model achieved considerable improvements in prediction accuracy compared to previous models, including Fourier decomposition, which Prophet uses to model seasonality patterns. A comparison was performed on a real-world dataset of pallet transport from a national-scale logistic network.
Register for our blog to get new articles as we release them. There are a number of forecasting packages written in R to choose from, each with their own pros and cons. For almost a decade, the forecast package has been a rock-solid framework for time series forecasting. However, within the last year or so an official updated version has been released named fable which now follows tidy methods as opposed to base R. More recently, modeltime has been released and this also follows tidy methods.
This work presents a hybrid and hierarchical deep learning model for mid-term load forecasting. The model combines exponential smoothing (ETS), advanced Long Short-Term Memory (LSTM) and ensembling. ETS extracts dynamically the main components of each individual time series and enables the model to learn their representation. Multi-layer LSTM is equipped with dilated recurrent skip connections and a spatial shortcut path from lower layers to allow the model to better capture long-term seasonal relationships and ensure more efficient training. A common learning procedure for LSTM and ETS, with a penalized pinball loss, leads to simultaneous optimization of data representation and forecasting performance. In addition, ensembling at three levels ensures a powerful regularization. A simulation study performed on the monthly electricity demand time series for 35 European countries confirmed the high performance of the proposed model and its competitiveness with classical models such as ARIMA and ETS as well as state-of-the-art models based on machine learning.
The explosion of time series data in recent years has brought a flourish of new time series analysis methods, for forecasting, clustering, classification and other tasks. The evaluation of these new methods requires a diverse collection of time series benchmarking data to enable reliable comparisons against alternative approaches. We propose GeneRAting TIme Series with diverse and controllable characteristics, named GRATIS, with the use of mixture autoregressive (MAR) models. We generate sets of time series using MAR models and investigate the diversity and coverage of the generated time series in a time series feature space. By tuning the parameters of the MAR models, GRATIS is also able to efficiently generate new time series with controllable features. In general, as a costless surrogate to the traditional data collection approach, GRATIS can be used as an evaluation tool for tasks such as time series forecasting and classification. We illustrate the usefulness of our time series generation process through a time series forecasting application.