关于java:STAT463-Homework-5

STAT463 Homework #5
due Monday, 2/18

1. Simulate an MA(2) series with θ1 = 1.0, θ2 = ?0.6, and n = 100 (normal error terms). Hint:
   see the example code in“4 arima plots and sim.R”
   (a) Display the sample ACF and PACF. Is the correct model identified?
   (b) Estimate the θ parameters using least-squares and then using maximum likelihood. Comment
   on any similarities or differences.
   (c) Now simulate 100 observations from this same MA(2) model except using error terms
   from a a chi-square distribution with 7 degrees of freedom.
   i. Repeat part (a) above for this data.
   ii. Repeat part (b) above for this data.
2. The data file named deere3 contains 57 consecutive values from a complex machine tool at
   Deere & Co. and represent deviations from a target value in units of ten millionths of an
   inch. Load the TSA package and then use data(deere3) to load the data.
   (a) Plot the data. Does it appear stationary?
   (b) Plot the ACF and PACF for the data. Which values for ARMA(p, q) are suggested?
   (c) Estimate the parameters of an AR(1) model for this series using maximum likelihood.
   Repeat this for an AR(2) model. Report the estimates, their standard errors, and the
   AIC values.
   (d) Simulate from both fitted models using the estimated parameters, with n = 57. Plot
   the simulated data for both models, and compare them to the original data.
   (e) Using your observations from parts (c) and (d), which of AR(1) or AR(2) would you
   prefer and why?
   (f) For the AR(1) model, use the estimated parameters to give an expression for yt
   . Use
   this expression to predict (forecast) the next value of y. In other words, find the numeric
   value of y58.

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