arXiv subjects

Rob J. Hyndman

Publications and source records attributed to Rob J. Hyndman.

12 recordsLinked to original sources

arXiv2026

Multivariate reconciliation for hierarchical time series

Some time series can be hierarchically organized into levels based on certain characteristics, such as geography or other attributes of interest. These series are referred to as hierarchical time series. Typically, forecasts are generated at all levels to ensure coherence, meaning that the forecasts should satisfy the same aggregation constraints as the observed data. Various approaches have been proposed to guarantee this coherence by using a set of base forecasts. The process through which these forecasts are adjusted to become coherent is known as forecast reconciliation. Similar to the univariate case, multivariate time series can also be structured hierarchically. However, all existing approaches are limited to a single variable. As a result, ensuring coherent forecasts requires reconciling each variable separately. However, this process does not account for correlations among multiple variables. To address this limitation, this paper proposes a multivariate reconciliation methodology that ensures coherent forecasts and incorporates relationships among variables. The proposed methodology was tested through numerical simulations, considering distinct scenarios within the series hierarchy and across multiple variables. Additionally, some base forecasting models were evaluated. The methodology was also applied to real employment data of admissions and dismissals in Brazil. The results demonstrated that multivariate reconciliation yielded more accurate outcomes than the other methods considered, both in simulated data and in practical applications.

stat.ME↗

arXiv2025

ggtime: A Grammar of Temporal Graphics

Visualizing changes over time is fundamental to learning from the past and anticipating the future. However, temporal semantics can be complicated, and existing visualization tools often struggle to accurately represent these complexities. It is common to use bespoke plot helper functions designed to produce specific graphics, due to the absence of flexible general tools that respect temporal semantics. We address this problem by proposing a grammar of temporal graphics, and an associated software implementation, 'ggtime', that encodes temporal semantics into a declarative grammar for visualizing temporal data. The grammar introduces new composable elements that support visualization across linear, cyclical, quasi-cyclical, and other granularities; standardization of irregular durations; and alignment of time points across different granularities and time zones. It is designed for interoperability with other semantic variables, allowing navigation across the space of visualizations while preserving temporal semantics.

cs.HC↗

arXiv2025

Good intentions, unintended consequences: exploring forecasting harms

Organizations worldwide that rely on data-driven approaches regularly employ forecasting methods to enhance their planning and decision-making processes. While extensive research has examined the harms associated with traditional machine learning applications, relatively little attention has been given to the ethical implications of time series forecasting. However, forecasting presents distinct ethical challenges due to its diverse organizational applications, varied objectives, and unique data processing, model development, and evaluation workflows. These distinctions complicate the direct application of existing machine learning harm taxonomies to common forecasting scenarios. To address this gap, we conduct multiple interviews with industry experts and academic researchers, systematically identifying and analyzing underexplored domains, use cases, and potential risks associated with forecasting. Our objective is to develop a novel taxonomy of forecasting-specific harms. Drawing inspiration from Microsoft Azure taxonomy for responsible innovation, we integrate a human-led inductive coding approach with AI-driven analysis to extract key categories of harm in forecasting. This taxonomy aims to support researchers and practitioners by fostering ethical reflection on their decision-making throughout the forecasting process. Additionally, we seek to establish a research agenda focused on identifying measures to mitigate potential harms in forecasting. By highlighting unique risks within forecasting, our work contributes to the broader discourse on machine learning ethics.

stat.OT↗

arXiv2025

Extreme Value Modelling of Feature Residuals for Anomaly Detection in Dynamic Graphs

Detecting anomalies in a temporal sequence of graphs can be applied is areas such as the detection of accidents in transport networks and cyber attacks in computer networks. Existing methods for detecting abnormal graphs can suffer from multiple limitations, such as high false positive rates as well as difficulties with handling variable-sized graphs and non-trivial temporal dynamics. To address this, we propose a technique where temporal dependencies are explicitly modelled via time series analysis of a large set of pertinent graph features, followed by using residuals to remove the dependencies. Extreme Value Theory is then used to robustly model and classify any remaining extremes, aiming to produce low false positives rates. Comparative evaluations on a multitude of graph instances show that the proposed approach obtains considerably better accuracy than TensorSplat and Laplacian Anomaly Detection.

cs.LG↗

arXiv2024

Forecast Linear Augmented Projection (FLAP): A free lunch to reduce forecast error variance

A novel forecast linear augmented projection (FLAP) method is introduced, which reduces the forecast error variance of any unbiased multivariate forecast without introducing bias. The method first constructs new component series which are linear combinations of the original series. Forecasts are then generated for both the original and component series. Finally, the full vector of forecasts is projected onto a linear subspace where the constraints implied by the combination weights hold. It is proven that the trace of the forecast error variance is non-increasing with the number of components, and mild conditions are established for which it is strictly decreasing. It is also shown that the proposed method achieves maximum forecast error variance reduction among linear projection methods. The theoretical results are validated through simulations and two empirical applications based on Australian tourism and FRED-MD data. Notably, using FLAP with Principal Component Analysis (PCA) to construct the new series leads to substantial forecast error variance reduction.

stat.ME↗

arXiv2023

Conditional normalization in time series analysis

Time series often reflect variation associated with other related variables. Controlling for the effect of these variables is useful when modeling or analysing the time series. We introduce a novel approach to normalize time series data conditional on a set of covariates. We do this by modeling the conditional mean and the conditional variance of the time series with generalized additive models using a set of covariates. The conditional mean and variance are then used to normalize the time series. We illustrate the use of conditionally normalized series using two applications involving river network data. First, we show how these normalized time series can be used to impute missing values in the data. Second, we show how the normalized series can be used to estimate the conditional autocorrelation function and conditional cross-correlation functions via additive models. Finally we use the conditional cross-correlations to estimate the time it takes water to flow between two locations in a river network.

stat.ME↗

arXiv2021

STR: Seasonal-Trend Decomposition Using Regression

We propose a new method for decomposing seasonal data: STR (a Seasonal-Trend decomposition using Regression). Unlike other decomposition methods, STR allows for multiple seasonal and cyclic components, covariates, seasonal patterns that may have non-integer periods, and seasonality with complex topology. It can be used for time series with any regular time index including hourly, daily, weekly, monthly or quarterly data. It is competitive with existing methods when they exist, but tackles many more decomposition problem than other methods allow. STR is based on a regularized optimization, and so is somewhat related to ridge regression. Because it is based on a statistical model, we can easily compute confidence intervals for components, something that is not possible with most existing decomposition methods (such as STL, X-12-ARIMA, SEATS-TRAMO, etc.). Our model is implemented in the R package stR, so can be applied by anyone to their own data.

stat.ME↗

arXiv2021

Monash Time Series Forecasting Archive

Many businesses and industries nowadays rely on large quantities of time series data making time series forecasting an important research area. Global forecasting models that are trained across sets of time series have shown a huge potential in providing accurate forecasts compared with the traditional univariate forecasting models that work on isolated series. However, there are currently no comprehensive time series archives for forecasting that contain datasets of time series from similar sources available for the research community to evaluate the performance of new global forecasting algorithms over a wide variety of datasets. In this paper, we present such a comprehensive time series forecasting archive containing 20 publicly available time series datasets from varied domains, with different characteristics in terms of frequency, series lengths, and inclusion of missing values. We also characterise the datasets, and identify similarities and differences among them, by conducting a feature analysis. Furthermore, we present the performance of a set of standard baseline forecasting methods over all datasets across eight error metrics, for the benefit of researchers using the archive to benchmark their forecasting algorithms.

cs.LG↗

arXiv2019

Anomaly Detection in High Dimensional Data

The HDoutliers algorithm is a powerful unsupervised algorithm for detecting anomalies in high-dimensional data, with a strong theoretical foundation. However, it suffers from some limitations that significantly hinder its performance level, under certain circumstances. In this article, we propose an algorithm that addresses these limitations. We define an anomaly as an observation that deviates markedly from the majority with a large distance gap. An approach based on extreme value theory is used for the anomalous threshold calculation. Using various synthetic and real datasets, we demonstrate the wide applicability and usefulness of our algorithm, which we call the stray algorithm. We also demonstrate how this algorithm can assist in detecting anomalies present in other data structures using feature engineering. We show the situations where the stray algorithm outperforms the HDoutliers algorithm both in accuracy and computational time. This framework is implemented in the open source R package stray.

stat.ML↗

arXiv2019

A feature-based framework for detecting technical outliers in water-quality data from in situ sensors

Outliers due to technical errors in water-quality data from in situ sensors can reduce data quality and have a direct impact on inference drawn from subsequent data analysis. However, outlier detection through manual monitoring is unfeasible given the volume and velocity of data the sensors produce. Here, we proposed an automated framework that provides early detection of outliers in water-quality data from in situ sensors caused by technical issues.The framework was used first to identify the data features that differentiate outlying instances from typical behaviours. Then statistical transformations were applied to make the outlying instances stand out in transformed data space. Unsupervised outlier scoring techniques were then applied to the transformed data space and an approach based on extreme value theory was used to calculate a threshold for each potential outlier. Using two data sets obtained from in situ sensors in rivers flowing into the Great Barrier Reef lagoon, Australia, we showed that the proposed framework successfully identified outliers involving abrupt changes in turbidity, conductivity and river level, including sudden spikes, sudden isolated drops and level shifts, while maintaining very low false detection rates. We implemented this framework in the open source R package oddwater.

stat.AP↗

arXiv2019

A framework for automated anomaly detection in high frequency water-quality data from in situ sensors

River water-quality monitoring is increasingly conducted using automated in situ sensors, enabling timelier identification of unexpected values. However, anomalies caused by technical issues confound these data, while the volume and velocity of data prevent manual detection. We present a framework for automated anomaly detection in high-frequency water-quality data from in situ sensors, using turbidity, conductivity and river level data. After identifying end-user needs and defining anomalies, we ranked their importance and selected suitable detection methods. High priority anomalies included sudden isolated spikes and level shifts, most of which were classified correctly by regression-based methods such as autoregressive integrated moving average models. However, using other water-quality variables as covariates reduced performance due to complex relationships among variables. Classification of drift and periods of anomalously low or high variability improved when we applied replaced anomalous measurements with forecasts, but this inflated false positive rates. Feature-based methods also performed well on high priority anomalies, but were also less proficient at detecting lower priority anomalies, resulting in high false negative rates. Unlike regression-based methods, all feature-based methods produced low false positive rates, but did not and require training or optimization. Rule-based methods successfully detected impossible values and missing observations. Thus, we recommend using a combination of methods to improve anomaly detection performance, whilst minimizing false detection rates. Furthermore, our framework emphasizes the importance of communication between end-users and analysts for optimal outcomes with respect to both detection performance and end-user needs. Our framework is applicable to other types of high frequency time-series data and anomaly detection applications.

stat.AP↗

arXiv2018

Predicting Sediment and Nutrient Concentrations in Rivers Using High Frequency Water Quality Surrogates

A particular focus of water-quality monitoring is the concentrations of sediments and nutrients in rivers, constituents that can smother biota and cause eutrophication. However, the physical and economic constraints of manual sampling prohibit data collection at the frequency required to capture adequately the variation in concentrations through time. Here, we developed models to predict total suspended solids (TSS) and oxidized nitrogen (NOx) concentrations based on high-frequency time series of turbidity, conductivity and river level data from low-cost in situ sensors in rivers flowing into the Great Barrier Reef lagoon. We fit generalized least squares linear mixed effects models with a continuous first-order autoregressive correlation to data collected traditionally by manual sampling for subsequent analysis in the laboratory, then used these models to predict TSS or NOx from in situ sensor water-quality surrogate data, at two freshwater sites and one estuarine site. These models accounted for both temporal autocorrelation and unevenly time-spaced observations in the data. Turbidity proved a useful surrogate of TSS, with high predictive ability at both freshwater and estuarine sites. NOx models had much poorer fits, even when additional covariates of conductivity and river level were included along with turbidity. Furthermore, the relative influence of covariates in the NOx models was not consistent across sites. Our findings likely reflect the complexity of dissolved nutrient dynamics in rivers, which are influenced by multiple and interacting factors including physical, chemical and biological processes, and the need for greater and better incorporation of spatial and temporal components within models.

stat.AP↗