A0248
Title: Comparison of interval time series
Authors: Ann Maharaj - Monash University (Australia) [presenting]
Paula Brito - Universidade do Porto (Portugal)
Paulo Teles - Universidade do Porto (Portugal)
Abstract: An interval time series (ITS) consists of intervals observed at consecutive time points, with each interval defined by its lower and upper bounds or by its centre and radius. In practical scenarios, analysing an ITS can offer more valuable insights into the variability between upper and lower bounds at each time point compared to analysing traditional time series with single values at each time point. We compare two ITS by assessing the statistical significance of differences in their underlying distributions. To perform hypothesis testing, we use the discrete wavelet transform (DWT) which decomposes a time series into a set of coefficients over several frequency bands or scales. We perform randomisation tests on the DWT of the radius and centre of the two ITS at different scales. Randomisation tests require uncorrelated observations. This condition is more or less satisfied because at each scale, the DWT coefficients are approximately uncorrelated with each other. The proposed test statistic is the ratio of the determinants of the covariance matrix of radius and centre DWTs of the two ITS, at each scale. This test statistic ensures that the variability between the upper and lower bounds is captured. Through simulation studies to assess its performance, reasonably good estimates of size and power of the test are observed. Application of the test to real interval time series demonstrates its practical utility in analysing and comparing ITS effectively.
