The effect of autocorrelated errors on change-detection statistics

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.