TY - JOUR

T1 - A test to compare interval time series

AU - Maharaj, Elizabeth Ann

AU - Brito, Paula

AU - Teles, Paulo

PY - 2021/6

Y1 - 2021/6

N2 - We compare two interval time series (ITS) by testing whether their underlying distributions are significantly different or not. To perform hypothesis testing, we make use of the discrete wavelet transform (DWT) which decomposes a time series into a set of coefficients over a number of frequency bands or scales. We obtain the DWT of the radius and centre of each of the two ITS at different scales, and perform randomisation tests. In order to use a randomisation test, the observations must be uncorrelated; this condition is more or less satisfied since at each scale, the DWT coefficients are approximately uncorrelated with each other. Our 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 of each ITS is encompassed. Simulation studies conducted to evaluate the performance of the test show reasonably good estimates of size and power under most conditions, and applications to real interval time series reveal the practical usefulness of this test.

AB - We compare two interval time series (ITS) by testing whether their underlying distributions are significantly different or not. To perform hypothesis testing, we make use of the discrete wavelet transform (DWT) which decomposes a time series into a set of coefficients over a number of frequency bands or scales. We obtain the DWT of the radius and centre of each of the two ITS at different scales, and perform randomisation tests. In order to use a randomisation test, the observations must be uncorrelated; this condition is more or less satisfied since at each scale, the DWT coefficients are approximately uncorrelated with each other. Our 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 of each ITS is encompassed. Simulation studies conducted to evaluate the performance of the test show reasonably good estimates of size and power under most conditions, and applications to real interval time series reveal the practical usefulness of this test.

KW - Discrete wavelet transform

KW - Interval time series

KW - Randomisation test

UR - http://www.scopus.com/inward/record.url?scp=85103325126&partnerID=8YFLogxK

U2 - 10.1016/j.ijar.2021.02.008

DO - 10.1016/j.ijar.2021.02.008

M3 - Article

AN - SCOPUS:85103325126

VL - 133

SP - 17

EP - 29

JO - International Journal of Approximate Reasoning

JF - International Journal of Approximate Reasoning

SN - 0888-613X

ER -