Kendall's tau with a blocking variable for time series data
LE3 .A278 2022
Master of Science
Mathematics and Statistics
Mathematics & Statistics
Kendall’s tau is a well known non-parametric statistic used for measuring the degree of dependency in bivariate data. This method has been well developed for data that is independent and identically distributed. However there is much less known about the case where data is not independently and identically distributed. The purpose of this thesis is to further expand the existing research of a weighted function of Kendall’s tau for data with the addition of a third variable, c, the blocking variable. In this thesis we will build on the existing research for Kendall’s tau with a blocking variable for the case when the bivariate data in the blocks is serially correlated time series data. As this new blocked function of Kendall’s depends on the variance of individual block Kendall’s tau estimates to compute the weighing function we will first focus on deriving a theoretical variance function for the standard Kendall’s tau when the data is AR(1) stationary time series data. With the theoretical variance established we will use bootstrapping techniques to estimate this variance allowing us to estimate the overall blocked Kendall’s tau measure. To make inference on the blocked Kendall’s tau estimate will use U-Statistics to develop a theorem on the asymptotic normal property of the blocked Kendall’s tau fuction. With this result we will construct confidence intervals using the moving block bootstrap for the true measure of blocked dependency. To evaluate the effectiveness of the weighted funciton we will demonstrate these confidence intervals for both the weighted function and the unweighted function. Finally these methods will be implemented in a case study demonstration with real blocked time series data.
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