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The effect of autocorrelated errors on change-detection statistics.

S M Tang1, I B Macneill

  • 1Department of Statistical and Actuarial Science, University of Western Ontario, N6A 5B9, London, Ontario, Canada.

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This study analyzes regression models with Autoregressive Moving Average (ARMA) errors. It adapts a change-detection statistic to identify shifts in regression parameters within these models.

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Area of Science:

  • Statistics
  • Time Series Analysis

Background:

  • Regression models are widely used but often assume independent errors.
  • Autocorrelated errors, common in time series data, violate this assumption and can impact model performance.
  • Autoregressive Moving Average (ARMA) processes are a standard way to model such autocorrelations.

Purpose of the Study:

  • To analyze regression models incorporating error terms generated by lower-order ARMA schemes.
  • To develop and adapt methods for parameter estimation in these complex models.
  • To address the challenge of detecting changes in regression parameters when errors are autocorrelated.

Main Methods:

  • Analysis of regression models with ARMA error structures.
  • Development of methods for estimating regression coefficients and ARMA process parameters.
  • Modification of MacNeill's (1978) change-detection statistic for ARMA processes.
  • Investigation of the impact of autocorrelated errors on the modified statistic.

Main Results:

  • Established methods for parameter estimation in regression models with ARMA errors.
  • Adapted a change-detection statistic suitable for ARMA error structures.
  • Provided insights into how autocorrelated errors affect change detection.

Conclusions:

  • The proposed methods offer a framework for analyzing regression models with ARMA errors.
  • The modified change-detection statistic is applicable to detecting parameter shifts in such models.
  • Understanding the influence of autocorrelated errors is crucial for robust statistical inference.