HW 1 (Due 1/27) From Chapter 1, 2 and notes:

1. Problem 2 page 20
2. Problem 3 page 20
3. Stationarity/Nonstationary
1. Find the mean and autocovariace function for the process X(t)=18.2+.4 u(t-2) + 2.3 u(t-3) + u(t) where u(t), t=…,-2,-1,0,1,2,… is a zero mean uncorrelated series.
2. Is this process a covariance stationary process? Explain
3. Is this process a strictly stationary process? Explain.
4. Explain why stationarity is a property of interest.
4. Stationarity/Nonstationarity. Suppose the same process as in problem three exhibits a quadratic structure in time, e.g. instead of the constant “18.2” we replace the non-stochastic component with “18.2 + .4t + .2t²”
1. Show that this new process in not stationary.
2. Transform the new process X(t) to a stationary process.

HW 2 (Due 2/3) From Chapter 1, 2 and notes:

1. Simulation study of the effect of autocorrelation on inference.
• Design and implement a simulation study that demonstrates the effect of positive and negative autocorrelation on estimation and prediction from a simple linear regression model.
2. Consider problem 9 on page 77.
• Fit a regression model to the series described assuming the errors are uncorrelated.
• Obtain the residuals from the regression equation and examine the autocorrelation structure of the residuals as well as the partial autocorrelation structure of the residuals. Comment on what see and the effect of any autocorrelation on the regression based inference. (The results of problem 1 should be helpful).
3. Problem 3 on page 76.

HW 3 (Due 2/10) From Chapter 2 and notes:

1. Show that an moving average model can be written as an autoregressive model of infinite order. What condition do you need on the coefficient of the moving average mnodel for this result to hold?
2. Problem 7 page 77.
3. Problem 8 page 77.