As noted in the course overview, you need to do a term project that consists of either

• a data analysis using some of the techniques we have discussed in class (assuming that you have a time series you wish to analyze);
• a critical review of the literature on one of the many aspects of spectral analysis that we won't be covering fully in class;
• some combination of a data analysis and critical review; or
• any idea that you come up with that will help you learn more about spectral analysis than what we have covered in class.

1. Please check with me about what you plan to do for the term project before you start it so that I can advise you whether or not it is appropriate. You can do so either
   • via e-mail,
   • by handing me a piece of paper with a description of what you want to do or
   • by speaking with me in person (after class would be fine).
   I would like to have some indication of what you intend to do by Friday, February 22nd.
2. I would like to meet with each of you for about 10 to 20 minutes sometime during the final week of lectures (from Monday, March 10th, to Friday, March 14th). I will pass around a sign-up sheet for specific times during the week before these meetings. The intent of the meetings is to discuss how your project is progressing and to give me a chance to give you some comments.
3. You should plan on giving an 8 to 10 minute in-class presentation on your project on Thursday, March 20th, between 8:30AM and 10:20AM.
4. The written portion of the project (see the guidelines below) is due no later than 3PM on Friday, March 21st. You can deliver it to me in person or hand it to the receptionist at APL, i.e., Henderson Hall (please tell the receptionist what it is you are handing him/her so that he/she doesn't pass your project along to the APL Furniture Request Committee, the default routing for miscellaneous pieces of paper). At 3PM on that Friday, I will gather all the projects that the receptionist has so kindly collected and will then disappear to a secret location, where I will commence reading the projects. This secret location has neither a phone nor a connection to the Internet, so pleas for mercy regarding turning in your project late will fall on deaf ears and darkened computer screens. (Note that it is not required that you turn in your projects just prior to the absolute deadline - I will be very happy to receive projects prior to March 21st!)

• The `meat' part of the project should be from 5 to (an upper limit of) 10 pages long (figures don't count toward the limit, but please keep the number of figures within reason).
• An important part of any writing you do is to keep in mind your intended audience. For the purposes of this project, you should assume that the audience is someone who is familiar with the material in Stat/EE 520. Thus, while it is fine to refer to, say, a `multitaper sdf estimate with 10 NW=6 dpss tapers' without needing to define what these terms mean, you should not assume that the reader is familiar with concepts specific to a particular problem area (e.g., turbulence theory, geophysics, machine monitoring, etc.). Your project should be as thorough and self-contained as possible -- while you can and should reference source material, there should be no need for a reader to track down this material in order to understand what you have written about. Except for what we have discussed in class, all symbols and terms should be defined. One way of thinking about structuring your project is to think of it as a potential addition to the class text or as a potential submission to a journal. For clarity, you might try to adopt the notation and terminology of the class text as much as possible even if this involves `translating' some of the notation in the source articles.
• If you choose to do a project on one or more papers concerning a particular aspect of spectral analysis of interest to you, make sure that you critically examine the papers that you read. A project that is little more than a synopsis or summary of one or two of papers (a `cut and paste' approach) is not what I would like to see. You should put as much original thinking into your project as possible (and, in accordance with what is required of any scholarly work, your written report must be original also, i.e., in your own words, with proper citation for ideas that are due to others, etc.). After initially reading a paper, carefully examine the authors' rationale for doing what they advocate. Ask yourself questions such as these:
  • Is the rationale for what the authors are proposing clear?
  • Are there any aspects that are arbitrary and in need of more solid justification?
  • What aspects can be improved upon?
  • Can what they have done be reproduced, or are important details missing?
  • If the papers include Monte Carlo studies, is it possible to verify what they did?
  • Are there any tests that you can think of that might point out potential weaknesses?
  In short, you should carefully examine and question all claims that the authors make.
• If you choose to do a data analysis (or a data analysis in conjunction with a literature review), make sure that you give enough information so that others could reproduce your results if they so desired. For example, if you compute a spectral estimate that depends on some parameter values, make sure you indicate how these values were set.
• Finally, please indicate an address (preferably a campus address) to which I can return your projects after the quarter is over (and don't forget to write your name on your project!).

1. P. Stoica and N. Sandgren (2006) `Smoothed nonparametric spectral estimation via cepsturm thresholding - Introduction of a method for smoothed nonparametric spectral estimation,' IEEE Signal Processing Magazine, 23(6), pp. 34-45. This paper expands considerably on some of the ideas behind the procedures that is discussed in Section 6.15 for automatically smoothing log spectral estimates.
2. M. Ghil, M.R. Allen, M.D. Dettinger, K. Ide, D. Kondrashov, M.E. Mann, A.W. Robertson, A. Saunders, Y. Tian, F. Varadi, and P. Yiou (2002), `Advanced Spectral Methods for Climatic Time Series,' Reviews of Geophysics, 40, 13 Sept (DOI 10.1029/2000RG000095). This paper discusses a number of spectral estimation techniques of interest in the analysis of climate time series. Some of the techniques have been covered in class (e.g., the multitaper method), both others have not (e.g., singular spectral analysis). An interesting project might be to take one of the uncovered techniques and to compare it to the ones that we have covered.
3. A. Mathias, F. Grond, R. Guardans, D. Seese, M. Canela and H. H. Diebner (2004), `Algorithms for Spectral Analysis of Irregularly Sampled Time Series,' Journal of Statistical Software, 11, Issue 2. We have only discussed how to estimate the spectral density function for equally sampled time series. The authors consider some schemes that work with irregularly sampled series, with application to some economic data and with an implementation of their methodology in the R language.
4. N. Choudhuri, S. Ghosal and A. Roy (2004), `Bayesian Estimation of the Spectral Density of a Time Series,' Journal of the American Statistical Association, 99, Issue 468, pp. 1050-1059. This paper considers a Bayesian approach to spectral density estimation. How does the proposed methodology compare to the techniques we have studied in class? What advantages and disadvantages does the Bayesian approach have over standard techniques?
5. A. Kowalski, F. Musial, P. Enck and K-T. Kalveram (2000), `Spectral Analysis of Binary Time Series: Square Waves vs. Sinusoidal Functions,' Biological Rhythm Research, 31(4), pp. 481-498. This paper compares Walsh spectral analysis and Fourier spectral analysis for binary-valued time series (see pages 161-4 of the course textbook for a brief introduction to Walsh spectral analysis).
6. P. M. T. Broersen (2002), `Automatic Spectral Analysis with Time Series Models,' IEEE Transactions on Instrumentation and Measurement, 51(2), pp. 211-216. How does the overall scheme advocated in this paper compare with what we have discussed in class? Note that there is a Matlab software package (ARMASA) that implements the techniques discussed in this article (the package may be freely used for scientific or educational purposes).
7. P. M. T. Broersen (2000), `Finite Sample Criteria for Autoregressive Order Selection,' IEEE Transactions on Signal Processing, 48, pp. 3550-3558. How do the order selection criteria discussed here compare with what is discussed in Chapter 9?
8. D. S. Coates and P. J. Diggle (1986), `Tests for Comparing Two Estimated Spectral Densities,' Journal of Time Series Analysis, 7, pp. 7-20; see also Section 4.8 of Diggle (1990), Time Series: A Biostatistical Introduction, Oxford: Oxford University Press. It would be interesting to apply this methodology to the two ice profile time series discussed starting on page 303 of the textbook.
9. M. J. Daniels and N. A. C. Cressie (2001), `A hierarchical approach to covariance function estimation for time series,' Journal of Time Series Analysis, 22, pp. 253-266. We have discussed a number of different estimators of the sdf, each of which corresponds to an estimator of the acvs. How does the estimator of the acvs discussed in this paper compare to these other estimators?
10. P. J. Diggle and I. al Wasel (1997), `Spectral Analysis of Replicated Biomedical Time Series,' Applied Statistics, 46, pp. 31-71. This paper discusses the sdf estimation problem when the data consist of a large number of quite short biomedical time series.
11. P. J. Diggle and N. I. Fisher (1991), `Nonparametric Comparison of Cumulative Periodograms,' Applied Statistics, 40, pp. 423-434. This paper considers a simple graphical method for comparing two periodograms and describes a nonparametric approach to testing the hypothesis that the two underlying spectra are the same. It would be of interest to see how this works on the two ice profile series.
12. S. Mirsaidi, G. A. Fleury and J. Oksman (1997), `LMS-Like AR Modeling in the Case of Missing Observations,' IEEE Transactions on Signal Processing, 45, pp. 1574-1583. How does this relate to the standard AR estimators in Chapter 9?
13. S. Ng and P. Perron (1996), `The Exact Error in Estimating the Spectral Density at the Origin,' Journal of Time Series Analysis, 17, pp. 379-408.
14. H. C. Ombao, J. A. Raz, R. L. Strawderman and R. von Sachs (2001), `A simple generalised cross-validation method of span selection for periodigram smoothing,' Biometrika, 88(4), pp. 1186-1192. This paper discusses a procedure for objectively selecting the bandwidth of the smoothing window for smoothing the periodogram. The procedure is based upon the idea of generalized cross-validation, which is an idea that can be used in tackling many parameter selection problems. How does this procedure compare to the two objective techniques that we discussed in Sections 6.14 and 6.15? Can this procedure be adjusted to work with sdf estimators other than the periodogram?
15. D.N. Politis and J.P. Romano (1995), `Bias-Corrected Nonparametric Spectral Estimation,' Journal of Time Series Analysis, 16, pp. 67-103. How does this proposed methodology contrast/compare with the methods in Chapters 6 and 7?
16. C. K. Yuen (1979), `On the Smoothed Periodogram Method for Spectrum Estimation,' Signal Processing, 1, pp. 83-86; and C. K. Yuen (1978), `Quadratic Windowing in the Segment Averaging Method for Power Spectrum Computation,' Technometrics, 20, pp. 195-200. This author is quite critical of the use of tapering. Is his/her critique valid?