node24 Forecasting Using the ARMA Model STAT 510 - Applied Time Series Analysis

# Node24 Forecasting Using the ARMA Model STAT 510 - Applied Time Series Analysis

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This is Google's cache of http://onlinecourses.science.psu.edu/stat510/node/24 . It is a snapshot of the page as it appeared on 29 Aug 2010 15:29:51 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 Forecasting Using the ARMA Model Submitted by gfj100 on Sun, 03/28/2010 - 15:33 Let's talk about forecasting an ARMA . We assume that we've started with an ARMA model (which is of course causal and invertible) and that we've estimated the parameters and they are EXACTLY right (not realistic -- but let's go with it right now.) The model is: We will assume for the moment that we know the coefficients of the model, the φ's and the θ's. Now, because it is causal and invertible, then if we know the φ's and the θ's, we also know the π's and the ψ's: (the causal representation) (the invertible representation) Recall that the ψ's are: and the π's are: . Assume we know how to calculate these. In practice, what we will have is data that goes from x 1 , . .. x n and what we want to do is to predict in future observations x n+ 1 , x n+ 2 ... x n+m .

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Let's define the tilde over x to mean: This is the conditional expectation: given my data up to
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## This note was uploaded on 09/10/2010 for the course STAT 510 at Penn State.

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Node24 Forecasting Using the ARMA Model STAT 510 - Applied Time Series Analysis

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