### Summer 2004 Final Project (Due August 5)

The purpose of this project is to provide a complete analysis of your data set. If you still don't have one or if the one you are analyzing has no structure (i.e. it is white noise or a random walk), please try to find another.

Write a function that does the analysis described below and email to me the function and the data set. Write a report (using Microsoft Word or some similar program; incorporate the plots into the report) that provides:

1. A description of the data, i.e. where it comes from, what the numbers represent, and what scientific questions are to be answered using time series analysis.

2. Descriptive statistics, i.e., plots of the data and the three descriptive statistics we discussed. Comment on what these plots mean about the data.

3. Transformations, i.e., if you feel that your data contain trends and/or cycles, try out any transformations that you feel may be useful. Provide descriptive statistics for the transformed data and comment on whether or not they indicate that the result is adequately detrended. If you feel that your data has disturbed periodicities, don't try to remove them using detrending.

4. A spectral density estimate for your detrended (if it was necessary) data. Plot the periodogram and use the WINDSP3 and ARSP functions to obtain possible estimates. Give any comments you can from scientific knowledge on which you feel is best and what the estimates tell you about your data.

5. Try to choose a full or subset ARMA model that adequately fits your detrended data. You will find the IDNEW function and the ARMASEL command useful in this regard. Make sure to provide the value of AIC for any model that you might think is valid. In order to verify the adequacy of your model, provide the following diagnostics:

1. Use SEASEST to get residuals from the model and give the results of the WNTEST function and the QTEST and BARTTEST functions for tests of white noise on the residuals.

6. Obtain forecasts of the next 24 values of your series using the model you found in (5). The PREDS function will be useful for doing this.

7. Write a summary of your results which answers the scientific questions posed in part (1).

Please be as brief as you can and please try to use as little paper as possible (for example, put more than one graph on a page if possible). It will be very difficult for me to read all of the projects so brevity will help me!

Good Luck and please let me know if you are having difficulty in completing the project.