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Applications of Random Rotations in R^n to test for serial correlation in time series data

  • Author / Creator
    Biswas, Amitakshar
  • Motivated by Elizabeth Meckes’ work on concentration inequalities using the group SO(n) (see [9]), this thesis explores the use of random rotations for detecting autocorrelation in time series data. Traditional tests like the Durbin Watson test assess autocorrelation by analyzing quadratic forms of residual vectors. Our new approach uses concentration inequalities associated with uniform measures on SO(n) to construct a test without strong distributional assumptions.

    We propose a new test statistic for autocorrelation in AR(1) processes, utilizing random rotations of sample autocorrelation function. By establishing a subgaussian concentration inequality, we derive a one-sided test with an
    upper bound for the p-value. Further refinement through beta adjustment enhances our p-value accuracy. We also generalize it to a two-sided test.

    This thesis provides comprehensive background material on group invariance, random rotations, AR(1) processes, and the Durbin-Watson test. Key results, including the concentration inequality proof and beta transformation application, are presented in detail. A simulation study confirms the effectiveness of our rotation test, highlighting its potential in practical statistical applications.

  • Subjects / Keywords
  • Graduation date
    Fall 2024
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/r3-ftmg-k264
  • License
    This thesis is made available by the University of Alberta Library with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.