arXiv subjects

Matthew A. Nunes

Publications and source records attributed to Matthew A. Nunes.

8 recordsLinked to original sources

arXiv2026

Multiscale Dynamic Dependence Estimation over Networks

In many settings, observed multivariate time series are often nonstationary in nature, i.e., their second order properties vary over time. An additional feature is that their cross-channel dependencies are structured by an underlying network. Together, they give rise to complex interactions between temporal dynamics and network topology. We propose Locally Stationary Wavelet processes on Networks (Net-LSW), a new framework for modelling multiscale, time-varying dependencies that explicitly incorporates the network structure. Unlike traditional multivariate approaches, the Net-LSW process encodes the graph directly in the covariance structure of its random increments. We introduce the concept of local partial correlation graph, mathematically connecting absent edges to zero entries in the time-scale dependent inverse wavelet spectral structure. For inference on the local cross-nodal (partial) dependence, we develop a novel subprocess-based estimation scheme and establish its consistency properties. This new pipeline for network-based nonstationary process modelling, complete with estimation and simulation capabilities that extend outside time-varying vector autoregressive models, is shown to accurately recover evolving dependence structures whilst respecting the underlying graph topology. The analysis of daily stock price volatilities across a global bank network captures multiscale, highly nonstationary dependencies and identifies time-varying systemic shifts during major financial shocks, including Brexit and the COVID-19 pandemic.

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arXiv2026

Network Time Series Models for Multivariate Volatility Forecasting

Realized volatility has become a standard tool for measuring latent variation in financial assets, and its forecasting is crucial for a wide range of financial applications. We propose a network-based model for forecasting a vector of realized variance processes through the heterogeneous autoregressive (HAR) approach. The generalised network HAR (GNHAR) model incorporates cross-sectional spillovers through a directed graph inferred from Granger-causality tests or connectedness indices, yielding a parsimonious multivariate time series model specification. In an application to ten equities over tranquil and crisis regimes, the proposed GNHAR model improves upon common HAR model benchmarks under both short- and long-term forecasting. We also compare the network-based specification when the jump-continuous decomposition or node-specific option-implied variances are considered. Finally, unlike overparameterised models, our approach yields a concise set of parameters that track the strengthening or weakening of cross-market dependencies, providing a time-varying quantitative assessment of market stability.

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arXiv2025

Network Estimation for Stationary Time Series

High-dimensional multivariate time series are common in many scientific and industrial applications, where the interest lies in identifying key dependence structure within the data for subsequent analysis tasks, such as forecasting. An important avenue to achieve this is through the estimation of the conditional independence graph via graphical models, although for time series data settings the underpinning temporal dependence can make this task challenging. In this article, we propose a novel wavelet domain technique that allows the data-driven inference of the (sparse) conditional independence graph of a high-dimensional stationary multivariate time series. By adopting the locally stationary wavelet modelling framework, we repose the estimation problem as a well-principled wavelet domain graphical lasso formulation. Theoretical results establish that our associated estimation scheme enjoys good consistency properties when determining sparse dependence structure in input time series data. The performance of the proposed method is illustrated using extensive simulations and we demonstrate its applicability on a real-world dataset representing hospitalisations of COVID-19 patients.

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arXiv2025

Long memory network time series

Many scientific areas, from computer science to the environmental sciences and finance, give rise to multivariate time series which exhibit long memory, or loosely put, a slow decay in their autocorrelation structure. Efficient modelling and estimation in such settings is key for a number of analysis tasks, such as accurate prediction. However, traditional approaches for modelling such data, for example long memory vector autoregressive processes, are challenging even in modest dimensions, as the number of parameters grows quadratically with the number of modelled variables. Additionally, in many practical data settings, the observed series is accompanied by a (possibly inferred) network that provides information about the presence or absence of between-component associations via the graph edge topology. This article proposes two new models for capturing the dynamics of long memory time series where a network is accounted for. Our approach not only facilitates the analysis of graph-structured long memory time series, but also improves computational efficiency over traditional multivariate long memory models by leveraging the inherent low-dimensional parameter space by adapting likelihood-based estimation algorithms to the network setting. Simulation studies show that our proposed estimation is more stable than traditional models, and is able to tackle data scenarios where current models fail due to computational challenges. While widely applicable, here we demonstrate the efficacy of our proposed models on datasets arising in environmental science and finance.

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arXiv2024

TrendLSW: Trend and Spectral Estimation of Nonstationary Time Series in R

The TrendLSW R package has been developed to provide users with a suite of wavelet-based techniques to analyse the statistical properties of nonstationary time series. The key components of the package are (a) two approaches for the estimation of the evolutionary wavelet spectrum in the presence of trend; and (b) wavelet-based trend estimation in the presence of locally stationary wavelet errors via both linear and nonlinear wavelet thresholding; and (c) the calculation of associated pointwise confidence intervals. Lastly, the package directly implements boundary handling methods that enable the methods to be performed on data of arbitrary length, not just dyadic length as is common for wavelet-based methods, ensuring no pre-processing of data is necessary. The key functionality of the package is demonstrated through two data examples, arising from biology and activity monitoring.

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arXiv2023

Automatic Locally Stationary Time Series Forecasting with application to predicting U.K. Gross Value Added Time Series under sudden shocks caused by the COVID pandemic

Accurate forecasting of the U.K. gross value added (GVA) is fundamental for measuring the growth of the U.K. economy. A common nonstationarity in GVA data, such as the ABML series, is its increase in variance over time due to inflation. Transformed or inflation-adjusted series can still be challenging for classical stationarity-assuming forecasters. We adopt a different approach that works directly with the GVA series by advancing recent forecasting methods for locally stationary time series. Our approach results in more accurate and reliable forecasts, and continues to work well even when the ABML series becomes highly variable during the COVID pandemic.

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arXiv2022

Modelling Time-Varying First and Second-Order Structure of Time Series via Wavelets and Differencing

Most time series observed in practice exhibit time-varying trend (first-order) and autocovariance (second-order) behaviour. Differencing is a commonly-used technique to remove the trend in such series, in order to estimate the time-varying second-order structure (of the differenced series). However, often we require inference on the second-order behaviour of the original series, for example, when performing trend estimation. In this article, we propose a method, using differencing, to jointly estimate the time-varying trend and second-order structure of a nonstationary time series, within the locally stationary wavelet modelling framework. We develop a wavelet-based estimator of the second-order structure of the original time series based on the differenced estimate, and show how this can be incorporated into the estimation of the trend of the time series. We perform a simulation study to investigate the performance of the methodology, and demonstrate the utility of the method by analysing data examples from environmental and biomedical science.

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arXiv2018

Dynamic detection of anomalous regions within distributed acoustic sensing data streams using locally stationary wavelet time series

Distributed acoustic sensing technology is increasingly being used to support production and well management within the oil and gas sector, for example to improve flow monitoring and production profiling. This sensing technology is capable of recording substantial data volumes at multiple depths within an oil well, giving unprecedented insights into production behaviour. However the technology is also prone to recording periods of anomalous behaviour, where the same physical features are concurrently observed at multiple depths. Such features are called `stripes' and are undesirable, detrimentally affecting well performance modelling. This paper focuses on the important challenge of developing a principled approach to identifying such anomalous periods within distributed acoustic signals. We extend recent work on classifying locally stationary wavelet time series to an online setting and, in so doing, introduce a computationally-efficient online procedure capable of accurately identifying anomalous regions within multivariate time series.

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