420Pr7 - Practice Problems 1. Consider the AR(1) model: (...

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Practice Problems 1. Consider the AR(1) model: ( Y t μ ) = φ ( Y t – 1 μ ) + e t where e t is a mean zero white noise process. Given the time series of 5 observations: y 1 = 10.1, y 2 = 9.3, y 3 = 9.4, y 4 = 9.8, y 5 = 10.6 a) Calculate the first two sample autocorrelation coefficients, r 1 and r 2 . ( Note: In practice reliable autocorrelation estimates are only obtained from series consisting of approximately 50 observations or more. ) b) Obtain the least-squares estimates for the AR(1) model parameters, ˆ and ˆ . 2. Consider the AR(1) model: ( Y t μ ) = ( Y t – 1 μ ) + e t where e t is a mean zero white noise process. The model has been fitted to a time series giving ˆ = 0.8, ˆ = 10.2, and 2 ± ˆ e = 0.25. The last five values of the series are y 96 = 10.1, y 97 = 9.3, y 98 = 9.4, y 99 = 9.8, y 100 = 10.6. Using the t = N = 100 as the forecast origin, forecasts the next three observations. Calculate the 95% probability limits for the next three observations.
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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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420Pr7 - Practice Problems 1. Consider the AR(1) model: (...

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