node23 PACF and Prediction STAT 510 - Applied Time Series Analysis

# Node23 PACF and Prediction STAT 510 - Applied Time Series Analysis

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This is Google's cache of http://onlinecourses.science.psu.edu/stat510/node/23 . It is a snapshot of the page as it appeared on 21 Jul 2010 13:21:08 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 PACF and Prediction Submitted by gfj100 on Sun, 03/28/2010 - 15:32 The ACF can be used to identify the order of a MA model. We know that the true ACF of a pure MA ( q ) model will drop to zero after the q th lag. (This is not always easy to see in practice due to the fluctuations in the empirical ACF.) An AR ( p ) or an ARMA ( p , q ) with p greater than or equal to one will generate an ACF plot that tails of exponentially. This is due to the causal property of these models. This is good in that we can tell the qualitative difference between MA ( q ) on one hand and the AR ( p ) / ARMA ( p , q ) on the other. If we think that the correct model is AR ( p ), we will not have a good guess for the order of this model. We would, therefore, like to design a plot which drops to zero after the p th lag when the true model is an AR ( p ). (For a MA ( q ) model, this new plot will trail off as the AR ( p ) does for the ACF.) This new plot is called the PACF, the partial autocorrelation function. The PACF at the h th lag is interpreted as the correlation between x t and x t-h where the linear dependency of the intervening lags ( x t- 1 , x t- 2 , . .. , x t-h+ 1 ) has been removed. Note that this is also how the parameters of a regression model are interpreted. Think about the difference between interpreting the regression models: x t = β 0 + β 1 t 2 and x t = β

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## This note was uploaded on 09/10/2010 for the course STAT 510 at Penn State.

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Node23 PACF and Prediction STAT 510 - Applied Time Series Analysis

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