# H9 - H9 cfw X t is called an autoregressive integrated...

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H9 {} t X is called an autoregressive integrated moving average (ARIMA) process of order (,,) pdq , denoted as ~ A R I M A ( , , ) t X , where is an integer, 1 d if its d -order difference is a casual AR (1 ) d tt YB =− X MA( , ) p q process, i.e., 2 () () ,{ } ~WN ( 0 , ) t BY B Z Z φ θσ = It is easy to see that an ARIMA( , , ) model is a special nonstationary ARMA( , ) p dq + model, *( ) ( ) B XB Z θ = , where ( )(1 ) d B BB φφ is a polynomial of order p d + . Example 1 model ARIMA(1,1,1) (1 .5 )(1 ) (1 .3 ) B BX BZ −−= + . Example 2 Differencing an ARMA( , ) p q results in a non-invertible process. Forecasts for an ARIMA( , , ) model, * 11 pd q t i ti t ii X XZ Z φθ +
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## This note was uploaded on 09/23/2009 for the course MATH 200 taught by Professor Gur during the Spring '09 term at Accreditation Commission for Acupuncture and Oriental Medicine.

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