Related papers: Point and probabilistic forecast reconciliation fo…

Hierarchical forecasting is a key problem in many practical multivariate forecasting applications - the goal is to simultaneously predict a large number of correlated time series that are arranged in a pre-specified aggregation hierarchy.…

We consider conformal prediction for multivariate data and focus on hierarchical data, where some components are linear combinations of others. Intuitively, the hierarchical structure can be leveraged to reduce the size of prediction…

An important task for any large-scale organization is to prepare forecasts of key performance metrics. Often these organizations are structured in a hierarchical manner and for operational reasons, projections of these metrics may have been…

We assess the advantage of combining univariate and multivariate portfolio risk forecasts with the aid of forecast reconciliation techniques. In our analyzes, we assume knowledge of portfolio weights, a standard for portfolio risk…

This paper proposes corrected forecast combinations when the original combined forecast errors are serially dependent. Motivated by the classic Bates and Granger (1969) example, we show that combined forecast errors can be strongly…

Multi-step forecasting is often described through a simple rule of thumb: recursive strategies are said to have high bias and low variance, while direct strategies are said to have low bias and high variance. We revisit this belief by…

In a sequential regression setting, a decision-maker may be primarily concerned with whether the future observation will increase or decrease compared to the current one, rather than the actual value of the future observation. In this…

Time series data appears in a variety of applications such as smart transportation and environmental monitoring. One of the fundamental problems for time series analysis is time series forecasting. Despite the success of recent deep time…

We present a scheme by which a probabilistic forecasting system whose predictions have poor probabilistic calibration may be recalibrated by incorporating past performance information to produce a new forecasting system that is demonstrably…

Multiple linear regression is a basic statistical tool, yielding a prediction formula with the input variables, slopes, and an intercept. But is it really easy to see which terms have the largest effect, or to explain why the prediction of…

When modeling sub-national mortality rates, we should consider three features: (1) how to incorporate any possible correlation among sub-populations to potentially improve forecast accuracy through multi-population joint modeling; (2) how…

I provide a unifying perspective on forecast evaluation, characterizing accurate forecasts of all types, from simple point to complete probabilistic forecasts, in terms of two fundamental underlying properties, autocalibration and…

Large collections of time series data are often organized into hierarchies with different levels of aggregation; examples include product and geographical groupings. Probabilistic coherent forecasting is tasked to produce forecasts…

Multivariate time series forecasting with hierarchical structure is widely used in real-world applications, e.g., sales predictions for the geographical hierarchy formed by cities, states, and countries. The hierarchical time series (HTS)…

In this paper we develop a novel method of combining many forecasts based on a machine learning algorithm called Graphical LASSO (GL). We visualize forecast errors from different forecasters as a network of interacting entities and…

The output of predictive models is routinely recalibrated by reconciling low-level predictions with known derived quantities defined at higher levels of aggregation. For example, models predicting turnout probabilities at the individual…

Many real-life applications involve simultaneously forecasting multiple time series that are hierarchically related via aggregation or disaggregation operations. For instance, commercial organizations often want to forecast inventories…

Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal…

Forecast reconciliation, an ex-post technique applied to forecasts that must satisfy constraints, has been a prominent topic in the forecasting literature over the past two decades. Recently, several efforts have sought to extend…

Time series forecasting has received wide interest from existing research due to its broad applications and inherent challenging. The research challenge lies in identifying effective patterns in historical series and applying them to future…