# 420Hw13 - STAT 420 (10 points) (due Friday, December 7, by...

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STAT 420 Fall 2007 Homework #13 (10 points) (due Friday, December 7, by 3:00 p.m.) 1. Given the time series 64 55 41 59 48 71 35 57 40 58 calculate r 1 and r 2 . ( Note: In practice reliable autocorrelation estimates are only obtained from series consisting of approximately 50 observations or more. ) 2. The model ( Y t μ ) = φ ( Y t – 1 μ ) + e t has been fitted to a time series giving ˆ = 0.6, ˆ = 5.0, and σ ˆ e 2 = 2.25. The last five values of the series are 5.5, 4.8, 4.5, 5.6, 4.7. Using the time of the last observation as the forecast origin, calculate the forecasts and approximate 95% probability limits for the next three observations. 3. Suppose that N observations from the AR(2) model gave the following sample ACF: r 1 = 1 ˆ = 0.8, r 2 = 2 ˆ = 0.5. Use the Yule-Walker equations to estimate 1 and 2 . 4. Consider the ARMA ( 1, 1 ) model ( Y t – 60 ) + 0.3 ( Y t – 1 – 60 ) = e t – 0.4 e t – 1 which was fitted to a time series where the last 10 values are

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## This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.

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420Hw13 - STAT 420 (10 points) (due Friday, December 7, by...

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