Sequential Procedures for Detecting Parameter Changes in a Time-Series Model

Michael L. Bagshaw · Richard A. Johnson

93 citations0/0 files storedJournal of the American Statistical Association

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Advanced Statistical Process Monitoring Fault Detection and Control Systems Time Series Analysis and Forecasting

Abstract

Procedures are proposed for monitoring forecast errors in order to detect changes in a time-series model. These procedures are based on likelihood ratio statistics which consist of cumulative sums. An extension of Page's method is presented which tests for changes in the parameter values of autoregressive integrated moving average (arima) models. The distributional properties of the statistics are approximated under the assumption that the series follows an integrated autoregressive moving average model. This approximation is based on the limiting Wiener process. An example is also given.

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References

1977Time Series Analysis: Forecasting and Control 1971Time Series Analysis Forecasting and Control.1954CONTINUOUS INSPECTION SCHEMES 1955A Test for a Change in a Parameter Occurring at an Unknown Point 1974The Effect of Serial Correlation on the Performance of CUSUM Tests 1965A Change in Level of a Non-Stationary Time Series 1971A Bayesian Approach to Short-term Forecasting 1965Cumulative Sum Techniques.

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2008Monitoring parameter change in AR ( p ) time series models 2002On-Line Statistical Process Control 2002Autocorrelated process monitoring using triggered cuscore charts 1984Monitoring and adjusting forecasts in the presence of additive outliers 1980Detecting change in a time-series (Corresp.)1994Statistics and Quality Improvement 1992Statistical Process Monitoring and Feedback Adjustment—A Discussion

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