Novel wavelet models for nonstationary time series.

在统计学中，如果一个时间序列是平稳的-这意味着它的统计属性，如平均值，不随时间变化-有大量的方法可用于分析时间序列。然而，通常情况下，时间序列是非平稳的。例如，一个时间序列可能会显示一个趋势-数据中的缓慢，长期运行的行为。非平稳时间序列出现在许多不同的领域，例如金融和环境统计，但这些类型的时间序列的研究较少。数值算法组（NAG）是该项目的工业合作伙伴，是一家为工业和学术界提供服务的数值软件公司。有一个明显的需求，不断更新和改进现有的软件库：统计软件用于非平稳时间序列也不例外。博士的主要重点是开发新的模型，为非平稳时间序列使用一个数学概念称为小波。子波是一种“小波”-它上下振荡，但时间很短。Wavelet允许我们通过在不同的尺度或频率下检查时间序列来捕获信息。博士的最终目标是开发一个非平稳时间序列模型，可用于估计时间序列的均值和方差。例如，这种模型可用于检验时间序列中是否存在趋势。与Numerical Algorithms Group（NAG）合作。

In statistics, if a time series is stationary - meaning that its statistical properties, like the mean, do not change over time - there is a huge wealth of methods available to analyse the time series. However, it is normally the case that a time series is nonstationary. For example, a time series might display a trend - slow, long-running behaviour in the data. Nonstationary time series arise in many diverse areas, for example finance and environmental statistics, but these types of time series are less well-studied.The Numerical Algorithms Group (NAG), the industrial partner of the project, is a numerical software company that provides services to both industry and academia. There is an obvious demand to continually update and improve existing software libraries: statistical software for use with nonstationary time series is no exception.The main focus of the PhD is to develop new models for nonstationary time series using a mathematical concept known as wavelets. A wavelet is a "little wave" - it oscillates up and down but only for a short time. Wavelets allow us to capture the information in a time series by examining them at different scales or frequencies. The ultimate aim of the PhD is to develop a model for nonstationary time series that can be used to estimate both the mean and variance in a time series. Such a model could then be used, for example, to test for the presence of trend in a time series. In partnership with Numerical Algorithms Group (NAG).