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Interrupted Time Series Analysis$
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David McDowall, Richard McCleary, and Bradley J. Bartos

Print publication date: 2019

Print ISBN-13: 9780190943943

Published to Oxford Scholarship Online: February 2021

DOI: 10.1093/oso/9780190943943.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use.date: 27 May 2022

ARIMA Algebra

ARIMA Algebra

Chapter:
(p.11) 2 ARIMA Algebra
Source:
Interrupted Time Series Analysis
Author(s):

David McDowall

Richard McCleary

Bradley J. Bartos

Publisher:
Oxford University Press
DOI:10.1093/oso/9780190943943.003.0002

Chapter 2 introduces ARIMA algebra. With a few exceptions, this material mirrors the authors’ earlier work. The chapter begins with stationary time series processes – white noise, moving average (MA), and autoregressive (AR) processes – and moves predictably to non-stationary and multiplicative (seasonal) models. Stationarity implies that the time series process operated identically in the past as it does in the present and that it will continue to operate identically in the future. Without stationarity, the properties of the time series would vary with the time frame and no inferences about the underlying process would be possible. A seasonally nonstationary process drifts or trends in annual steps. The “best” seasonal model structure is the one that transforms the series to white noise with the fewest number of parameters.

Keywords:   Lag operator, backshift operator, autoregressive AR, moving average MA, stationary

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