The effects of model parameter deviations on the variance of a linearly filtered time series

Daniel W. Apley, Hyun Cheol Lee

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider a general linear filtering operation on an autoregressive moving average (ARMA) time series. The variance of the filter output, which is an important quantity in many applications, is not known with certainty because it depends on the true ARMA parameters. We derive an expression for the sensitivity (i.e., the partial derivative) of the output variance with respect to deviations in the model parameters. The results provide insight into the robustness of many common statistical methods that are based on linear filtering and also yield approximate confidence intervals for the output variance. We discuss applications to time series forecasting, statistical process control, and automatic feedback control of industrial processes.

Original languageEnglish (US)
Pages (from-to)460-471
Number of pages12
JournalNaval Research Logistics
Volume57
Issue number5
DOIs
StatePublished - Aug 1 2010

Keywords

  • Autoregressive moving average model
  • Control chart
  • Parameter uncertainty
  • Robustness
  • Time series forecasting

ASJC Scopus subject areas

  • Modeling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research

Fingerprint Dive into the research topics of 'The effects of model parameter deviations on the variance of a linearly filtered time series'. Together they form a unique fingerprint.

Cite this