node25 Building ARIMA Models STAT 510 - Applied Time Series Analysis

# Node25 Building ARIMA Models STAT 510 - Applied Time Series Analysis

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This is Google's cache of http://onlinecourses.science.psu.edu/stat510/node/25 . It is a snapshot of the page as it appeared on 20 Jul 2010 17:45:49 GMT. The current page could have changed in the meantime. Learn more Text-only version STAT 510 - Applied Time Series Analysis ANGEL Department of Statistics Eberly College of Science Home // Section 2: Time Domain Models Building ARIMA Models Submitted by gfj100 on Sun, 03/28/2010 - 15:35 When we discussed exploratory data analysis and smoothing that we often began with a model such as: x t = μ t + y t where μ t was a deterministic component (trend) and y t was a stationary zero-mean process. If we assume μ t was of the form β 0 + β 1 t , then differencing yields: x t = β 1 + y t which will be a stationary time series. In general, if μ t is a polynomial in t , such as

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β 0 + β 1 t ... +
β 0 + β p t p , then: k x t = β k + k y t Now, these are not the only choices for μ t that will be "fixed" by differencing. Another might be: μ t = μ t- 1 + v t where v t is stationary. The x t = μ t + y t will be made stationary by differencing. Let's also get specific about y t and the definition of ARIMA . Definition : A process is ARIMA ( p , d , q ) if: d x t is ARMA ( p , q ). If the mean of d x t is zero the we can write the model as: φ( B ) d x t = θ( B ) w t If a mean does exist then we can write: φ( B ) d x t = α + θ( B ) w t where α = μ(1 − φ 1 − . .. − φ p ). We do need to be careful with our thinking however. Let’s assume that our data is generated by the following model: x t =

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β 0 + β 1 t + y t where y t = φ 1 y t- 1 + φ 2 y t- 2 + w t . Now, if we look at
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## This note was uploaded on 09/10/2010 for the course STAT 510 at Pennsylvania State University, University Park.

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Node25 Building ARIMA Models STAT 510 - Applied Time Series Analysis

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