LS2W: Implementing the Locally Stationary 2D Wavelet Process Approach in R

Locally stationary process representations have recently been proposed and applied to both time series and image analysis applications. This article describes an implementation of the locally stationary two-dimensional wavelet process approach in R. This package permits construction of estimates of spatially localized spectra and localized autocovariance which can be used to characterize structure within images.

pinktoe: Semi-automatic Traversal of Trees

Tree based methods in S or R are extremely useful and popular. For simple trees and memorable variables it is easy to predict the outcome for a new case using only a standard decision tree diagram. However, for large trees or trees where the variable description is complex the decision tree diagram is often not enough. This article describes pinktoe: an R package containing two tools to assist with the semiautomatic traversal of trees. The PT tool creates a widget for each node to be visited in the tree that is needed to make a decision and permits the user to make decisions using radiobuttons. The pinktoe function generates a suite of HTML and Perl files that permit a CGI-enabled website to issue step-by-step questions to a user wishing to make a prediction using a tree

Technical appendix to locally stationary wavelet fields with application to the modelling and analysis of image texture.

This report is an appendix to the paper Locally stationary wavelet fields with application to the modelling and analysis of image texture, providing proofs for all the major results

Leveraging Non-Decimated Wavelet Packet Features and Transformer Models for Time Series Forecasting

This article combines wavelet analysis techniques with machine learning methods for univariate time series forecasting, focusing on three main contributions. Firstly, we consider the use of Daubechies wavelets with different numbers of vanishing moments as input features to both non-temporal and temporal forecasting methods, by selecting these numbers during the cross-validation phase. Secondly, we compare the use of both the non-decimated wavelet transform and the non-decimated wavelet packet transform for computing these features, the latter providing a much larger set of potentially useful coefficient vectors. The wavelet coefficients are computed using a shifted version of the typical pyramidal algorithm to ensure no leakage of future information into these inputs. Thirdly, we evaluate the use of these wavelet features on a significantly wider set of forecasting methods than previous studies, including both temporal and non-temporal models, and both statistical and deep learning-based methods. The latter include state-of-the-art transformer-based neural network architectures. Our experiments suggest significant benefit in replacing higher-order lagged features with wavelet features across all examined non-temporal methods for one-step-forward forecasting, and modest benefit when used as inputs for temporal deep learning-based models for long-horizon forecasting

New tools for network time series with an application to COVID-19 hospitalisations

Network time series are becoming increasingly important across many areas in science and medicine and are often characterised by a known or inferred underlying network structure, which can be exploited to make sense of dynamic phenomena that are often high-dimensional. For example, the Generalised Network Autoregressive (GNAR) models exploit such structure parsimoniously. We use the GNAR framework to introduce two association measures: the network and partial network autocorrelation functions, and introduce Corbit (correlation-orbit) plots for visualisation. As with regular autocorrelation plots, Corbit plots permit interpretation of underlying correlation structures and, crucially, aid model selection more rapidly than using other tools such as AIC or BIC. We additionally interpret GNAR processes as generalised graphical models, which constrain the processes' autoregressive structure and exhibit interesting theoretical connections to graphical models via utilization of higher-order interactions. We demonstrate how incorporation of prior information is related to performing variable selection and shrinkage in the GNAR context. We illustrate the usefulness of the GNAR formulation, network autocorrelations and Corbit plots by modelling a COVID-19 network time series of the number of admissions to mechanical ventilation beds at 140 NHS Trusts in England & Wales. We introduce the Wagner plot that can analyse correlations over different time periods or with respect to external covariates. In addition, we introduce plots that quantify the relevance and influence of individual nodes. Our modelling provides insight on the underlying dynamics of the COVID-19 series, highlights two groups of geographically co-located `influential' NHS Trusts and demonstrates superior prediction abilities when compared to existing techniques