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A Very British AffairBox and Jenkins: Modelling Seasonal Time Series and Transfer Function Analysis

A Very British Affair: Box and Jenkins: Modelling Seasonal Time Series and Transfer Function... [As was developed in some detail in Chapter 6, the Box-Jenkins approach to modelling time series revolves around the ARMA process which has an eventual forecast function that is the solution to the difference equation , where B is understood to operate on l (cf. §6.39). Box and Jenkins (1970, chapter 9) argued that, to be able to represent seasonal behaviour, the forecast function would need to trace out a periodic pattern. This could be achieved by allowing the autoregressive operator φ(B) to consist of a mixture of sines and cosines, possibly mixed with polynomial terms to allow for changes in the level of xt and changes in the seasonal pattern. For example, a forecast function containing a sine wave with a 12-month period, which is adaptive in both phase and amplitude, will satisfy the difference equation The operator has roots of exp (± i2π/12) on the unit circle and is thus homogeneously non-stationary. Box and Jenkins pointed out, however, that periodic behaviour would not necessarily be represented parsimoniously by mixtures of sines and cosines.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Very British AffairBox and Jenkins: Modelling Seasonal Time Series and Transfer Function Analysis

Part of the Palgrave Advanced Texts in Econometrics Book Series
Mills, Terence C.
Springer Journals — Nov 2, 2015
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23 pages

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Publisher
Palgrave Macmillan UK
Copyright
© Palgrave Macmillan, a division of Macmillan Publishers Limited 2013
ISBN
978-1-349-35027-8
Pages
216 –239
DOI
10.1057/9781137291264_7
Publisher site
See Chapter on Publisher Site

Abstract

[As was developed in some detail in Chapter 6, the Box-Jenkins approach to modelling time series revolves around the ARMA process which has an eventual forecast function that is the solution to the difference equation , where B is understood to operate on l (cf. §6.39). Box and Jenkins (1970, chapter 9) argued that, to be able to represent seasonal behaviour, the forecast function would need to trace out a periodic pattern. This could be achieved by allowing the autoregressive operator φ(B) to consist of a mixture of sines and cosines, possibly mixed with polynomial terms to allow for changes in the level of xt and changes in the seasonal pattern. For example, a forecast function containing a sine wave with a 12-month period, which is adaptive in both phase and amplitude, will satisfy the difference equation The operator has roots of exp (± i2π/12) on the unit circle and is thus homogeneously non-stationary. Box and Jenkins pointed out, however, that periodic behaviour would not necessarily be represented parsimoniously by mixtures of sines and cosines.]

Published: Nov 2, 2015

Keywords: Transfer Function; Impulse Response; Noise Model; Step Response; Transfer Function Model

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