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node22 ARMA and ARIMA STAT 510 - Applied Time Series Analysis

# Node22 ARMA and ARIMA STAT 510 - Applied Time Series Analysis

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This is Google's cache of http://onlinecourses.science.psu.edu/stat510/node/22 . It is a snapshot of the page as it appeared on 21 Jul 2010 12:36:55 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 ARMA and ARIMA Submitted by gfj100 on Sun, 03/28/2010 - 15:30 ARMA Definition x t is ARMA ( p , q ) if x t is stationary and can be written as: ARMA Models We remind ourselves what φ( B ) and θ( B ) are in this context: Note that φ( B ) has negative signs because we are moving these x t from the right side to the left side. Applying the backshift operators and moving all the terms with parameters to the right-hand side, we obtain: and this is the Auto Regressive Moving Average model ( ARMA ). The notation typically used is ARMA ( p , q ). Therefore, an ARMA (1, 1) would only include the φ 1 x t- 1 and the θ 1 w t- 1 terms (in addition to w t ). An

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ARMA (2, 1) would include two φ terms, φ 1 x t- 1 and φ 2 x t- 2 , and one MA term, θ 1 w t- 1 . The notation simply tells you the order of the AR part and the MA part of the model. You always include w t with no coefficient, (but recall w t always includes a variance parameter.) A Troublesome Example - Parameter Redundancy Suppose that the model for your data is white noise. If this is true for every
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