TIME SERIES ANALYSIS HOMEWORK- STATISTICS

STAT463 Homework #5 due Wednesday, 2/22 1.

(adapated from Cryer & Chan Exercise 7.27 ) Exhibit 6.31 on page 139 suggested specifying either an AR(1) or possibly an AR(4) model for the difference of the logarithms of the oil price series. The data are available with the command data(oil.price)(TSA package should be loaded first).

(a) Estimate both of these models using maximum likelihood and compare it with the results using the AIC criteria.

(b) Exhibit 6.32 on page 140 suggested specifying an MA(1) model for the difference of the logs. Estimate this model by maximum likelihood and compare to your results in part (a).

2.

(adapted from Cryer & Chan Exercise 7.28 ) The data file nameddeere3contains 57 con- secutive 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?