8. Transfer Function Models

  1. Søren Bisgaard and
  2. Murat Kulahci

Published Online: 31 MAY 2011

DOI: 10.1002/9781118056943.ch8

Time Series Analysis and Forecasting by Example

Time Series Analysis and Forecasting by Example

How to Cite

Bisgaard, S. and Kulahci, M. (2011) Transfer Function Models, in Time Series Analysis and Forecasting by Example, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118056943.ch8

Author Information

  1. Technical University of Denmark

Publication History

  1. Published Online: 31 MAY 2011
  2. Published Print: 5 JUL 2011

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780470540640

Online ISBN: 9781118056943



  • autocorrelation;
  • Box-Jenkins;
  • gas furnace data;
  • input-output relationship;
  • noise model;
  • transfer function


This chapter focuses on the unidirectional relationship between an input and an output, both of which are time series. It discusses how to analyze the relationship between an input and an output of a process. The chapter demonstrates how to assess delayed dynamic relationships using the theory originally developed by Box and Jenkins. The author uses an example to demonstrate step-by- step how to assess the form of the input-output relationship for a relatively complex process. The chapter describes the transfer function-noise model to describe the dynamic relationship between the output and the input with added noise. In that model, the author assumes that the noise term was most likely autocorrelated. The chapter summarizes the steps followed in the analysis of the gas furnace data in order to provide a general overview of the methodology proposed by BJR.

Controlled Vocabulary Terms

autocorrelation; white noise