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Slides on ARIMA models--Robert Nau

1 Lecture notes on forecastingRobert NauFuqua School of BusinessDuke UniversityIntroduction to ARIMA models Nonseasonal ~ (c) 2014 by Robert Nau, all rights reservedARIMA models Auto-Regressive Integrated Moving Average Are an adaptation of discrete-time filtering methods developed in 1930 s-1940 s by electrical engineers (Norbert Wiener et al.) Statisticians George Box and Gwilym Jenkins developed systematic methods for applying them to business & economic data in the 1970 s (hence the name Box-Jenkins models )2 What ARIMA stands for A series which needs to be differenced to be made stationary is an integrated (I) series Lags of the stationarized series are called auto-regressive (AR) terms Lags of the forecast errors are called moving average (MA) terms We ve already studied these time series tools separately.

3 Construction of an ARIMA model 1. Stationarize the series, if necessary, by differencing (& perhaps also logging, deflating, etc.) 2. Study the pattern of autocorrelations and partial autocorrelations to determine if lags of the stationarized series and/or lags of the forecast errors should be included

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