相关论文: Nonlinear reconciliation: Error reduction theorems

Methods for forecasting time series adhering to linear constraints have seen notable development in recent years, especially with the advent of forecast reconciliation. This paper extends forecast reconciliation to the open question of…

Forecast reconciliation adjusts independently generated forecasts so that they satisfy some known constraints. While probabilistic forecast reconciliation is well established for linear constraints, some practical forecasting problems…

Forecast reconciliation is a post-forecasting process aimed to improve the quality of the base forecasts for a system of hierarchical/grouped time series (Hyndman et al., 2011). Contemporaneous (cross-sectional) and temporal hierarchies…

Forecast reconciliation is the post-forecasting process aimed to revise a set of incoherent base forecasts into coherent forecasts in line with given data structures. Most of the point and probabilistic regression-based forecast…

In numerous applications, it is required to produce forecasts for multiple time-series at different hierarchy levels. An obvious example is given by the supply chain in which demand forecasting may be needed at a store, city, or country…

Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…

In this paper, we propose a machine learning approach for forecasting hierarchical time series. When dealing with hierarchical time series, apart from generating accurate forecasts, one needs to select a suitable method for producing…

Hierarchical time series are common in several applied fields. The forecasts for these time series are required to be coherent, that is, to satisfy the constraints given by the hierarchy. The most popular technique to enforce coherence is…

Hierarchical forecasting with reconciliation requires forecasting values of a hierarchy (e.g.~customer demand in a state and district), such that forecast values are linked (e.g.~ district forecasts should add up to the state forecast).…

We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…

Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a…

Forecast reconciliation is a post-forecasting process that involves transforming a set of incoherent forecasts into coherent forecasts which satisfy a given set of linear constraints for a multivariate time series. In this paper we extend…

This paper focuses on forecasting hierarchical time-series data, where each higher-level observation equals the sum of its corresponding lower-level time series. In such contexts, the forecast values should be coherent, meaning that the…

The practical importance of coherent forecasts in hierarchical forecasting has inspired many studies on forecast reconciliation. Under this approach, so-called base forecasts are produced for every series in the hierarchy and are…

We propose to estimate the weight matrix used for forecast reconciliation as parameters in a general linear model in order to quantify its uncertainty. This implies that forecast reconciliation can be formulated as an orthogonal projection…

Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…

Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be…

As the popularity of hierarchical point forecast reconciliation methods increases, there is a growing interest in probabilistic forecast reconciliation. Many studies have utilized machine learning or deep learning techniques to implement…

We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…

Although contrastive and other representation-learning methods have long been explored in vision and NLP, their adoption in modern time series forecasters remains limited. We believe they hold strong promise for this domain. To unlock this…