Wavelet Methods for Analysing Locally Stationary Time Series

Fitting models for, and simulation of, trend locally stationary wavelet (TLSW) time series models, which take account of time-varying trend and dependence structure in a univariate time series. The TLSW model, and its estimation, is described in McGonigle, Killick and Nunes (2022a) , (2022b) . Further information regarding the use of the package, along with detailed examples, can be found in McGonigle, Killick and Nunes (2025) . New users will likely want to start with the TLSW function.

TrendLSW

Implements wavelet methods for analysis of nonstationary time series. See

McGonigle, E. T., Killick, R., and Nunes, M. (2022). Trend locally stationary wavelet processes. Journal of Time Series Analysis, 43(6), 895-917.

McGonigle, E. T., Killick, R., and Nunes, M. (2022). Modelling time-varying first and second-order structure of time series via wavelets and differencing. Electronic Journal of Statistics, 6(2), 4398-4448.

for full details.

Installation

You can install the released version of TrendLSW from CRAN with:

install.packages("TrendLSW")

You can install the development version of TrendLSW from GitHub with:

devtools::install_github("https://github.com/EuanMcGonigle/TrendLSW")

Usage

For detailed examples, see the help files within the package. We can generate a small example for performing trend and spectrum estimation as follows:

library(TrendLSW)

set.seed(1)

noise <- rnorm(512) * c(seq(from = 1, to = 3, length = 256), seq(from = 3, to = 1, length = 256))
trend <- seq(from = 0, to = 5, length = 512)
x <- trend + noise

Apply the TLSW function: