AbstractThis thesis presents new methods in time series analysis focusing on three areas: stationarity testing, network autoregression modelling, and local white noise testing.
We begin by describing a bespoke stationarity test for use when univariate data has missing observations. This test is based upon a second-generation wavelet method known as the non-decimated lifting transform, which allows for the analysis of irregularly spaced data. The variance of a spectral estimate linked to the non-decimated lifting transform is used in our test statistic, and compared to the same quantity calculated on simulated stationary samples to assess signiﬁcance.
The second section provides a model for multivariate time series observed on nodes of a network. Our model allows such data to be modelled with few parameters, and is shown to be a useful modelling tool for predicting multivariate time series. A stationarity condition and consistency results for this model are described, and results are generated using our software package for ﬁtting this model.
A local white noise test is motivated in the third section, which can be applied at many diﬀerent positions in a time series. The smoothed wavelet periodogram forms the basis of our test, and relevant distributional results for its implementation are described, including new results of Haar and Shannon wavelet quantities. Diﬀerent test statistics are investigated, each based upon testing equality of the periodogram at diﬀerent scales.
|Date of Award||25 Jun 2019|
|Supervisor||Guy Nason (Supervisor)|