# 420Pr6 - Practice Problems 1 Consider the AR(1 model Yt = Yt 1 et where e t is a mean zero white noise process Given the time series of 5

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/10/2009 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois at Urbana–Champaign.

### Page1 / 4

420Pr6 - Practice Problems 1 Consider the AR(1 model Yt = Yt 1 et where e t is a mean zero white noise process Given the time series of 5

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online