ch04 - Chapter 4: Estimation in the Time Domain Li Chen...

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Unformatted text preview: Chapter 4: Estimation in the Time Domain Li Chen Department of Mathematics University of Bristol 1 / 10 Outline Fitting an ARIMA process to an observed time series proceeds in three stages: 1. identification of the order ( p , d , q ), 2. estimation of the model parameters, 3. diagnostic checking of the fitted model. In this chapter we will learn: I modeling an autoregressive process (AR) I modeling a moving average process (MA) I modeling an ARIMA process 2 / 10 4.1 Modeling AR( p ) Given x 1 , . . . , x N suppose we identify the process as an AR( p ). There are two steps: (a) identifying p , (b) estimating parameters { 1 , . . . , p } . We will consider (b) first. Suppose we know p . Then we will use the model X t- = 1 ( X t- 1- ) + + p ( X t- p- ) + Z t , t = p + 1 , . . . , N to model a time series { X t } with mean . 3 / 10 4.1.1 Estimating the parameters of an AR process Least squares estimation Given N observations x 1 , . . . , x N the parameters...
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ch04 - Chapter 4: Estimation in the Time Domain Li Chen...

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