As outlined briefly 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 data you wish to analyze);
• a simulation study;
• some methodological or theoretical research;
• a critical review of the literature on one of the many aspects of wavelets that we won't be covering fully in class;
• some combination of the above; or,
• subject to my approval, any idea that you come up with that will help you learn more about wavelets 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 (dbp@uw.edu),
   • 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, 11 May.
2. Plan on giving a short (5 to 10 minute) in-class presentation about your project during either one of the final two class periods (Wednesday, 30 May, and Friday, 1 June, 12:30PM to 1:20PM), or the time slot allocated for a final exam for the class (Thursday, 7 June, starting at 8:30AM).
3. The written portion of the project (see the guidelines below) is due no later than 2PM on Friday, 8 June. You can place it in my mailbox in the main office (Padelford, C-310) of the Department of Statistics (note that it is not required that you turn in your projects just prior to the absolute deadline - I would be overjoyed to receive projects prior to June 8!!). I will be in Padelford C-310 from 1PM to 2PM on Friday, 8 June, if you want to hand me your written report rather than putting it into my mailbox. Also please e-mail me (dbp@uw.edu) a PDF version of your written report (please do not send a Word version - my Mac has a hard time digressing Word documents).

• The `meat' part of the project should be from 5 to (an upper limit of) 10 double-spaced single-column pages using a font size that won't strain my eyes (a 9 point font is recommended; 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 530. Thus, while it is fine to refer to, say, a "level j = 7 DWPT based upon the LA(8) wavelet" without needing to define what these terms mean, you should not assume familiarity with concepts specific to a particular problem area (e.g., turbulence theory, communications theory, 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 notes or as a potential submission to a journal. For clarity, try to adopt the notation and terminology used in class 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 wavelets 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 what they are advocating. 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 (i.e., computer experiments involving pseudo-random numbers), 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 make use of a procedure 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!).

  [added to list on 23 April]: `Locally Stationary Wavelet Packet Processes: Basis Selection and Model Fitting' by Alessandro Cardinali and Guy P. Nason (2017), Journal of Time Series Analysis, Volume 38, Number 2, pp. 151-174. We discussed the basic ideas behind wavelet packets in class. This paper uses these to define a class of nonstationary processes that are useful as models for certain economic time series such as the S&P 500 index. A good project would be to extract the main ideas in the paper and to replicate as many as possible of the simulation examples described in Section 6 of the paper.

  [added to list on 22 April]: `Tests for serial correlation of unknown form in dynamic least squares regression with wavelets' by Meiyu Li and Ramazan Gencay (2017), Economics Letters, Volume 155, pp. 104-110. This paper looks into wavelet-based multi-scale tests for serial correlation in unobservable errors of unknown form in a linear dynamic regression model. A good project would be to extract the main ideas in the paper and to replicate as many of the results as possible described in Section 4 (Monte Carlo simulations) of the paper.

  [added to list on 22 April]: `Estimation of Long Memory in Volatility using Wavelets' by Lucie Kraicova and Jozef Barunik (2017), Studies in Nonlinear Dynamics and Econometrics, Volume 21, Number 3, 22 pages. Late in the quarter we will be discussing wavelet-based estimation of parameters in time series models that can take into account long-memory dependence. The models we will be looking are fairly simple ones. This paper looks at a wavelet-based approach for models with much more complexity that are of interest for economic time series. A good project would be to contract the methodology in the paper with what will be discussed in class and to replicate some of the extensive Monte Carlo study the authors undertook to validate their methodology.

  [added to list on 22 April]: `A Wavelet-based Multivariate Multiscale Approach for Forecasting' by Antonio Rua (2017), International Journal of Forecasting, Volume 33, Number 3, pp. 581-590. This paper looks at wavelet-based forecasting of GNP growth and inflation in the United States by merging the multiscale aspect of the wavelet transform with factor models. A good project would be to extract the author's main ideas and to replicate as much of the Monte Carlo simulation study in Section 3.2 of the paper as possible (replication of the data analysis in Section 4 would be another goal if obtaining the data is not too time consuming).

  [added to list on 21 April]: `Catching the Curl: Wavelet Thresholding Improves Forward Curve Modelling' by Gabriel J. Power, James Eaves, Calum Turvey and Dmitry Vedenov (2017), Economic Modelling, Volume 64, pp. 312-321. This paper looks at wavelet-based denoising in the context of a state space model as applied to a particular economic time series. A good project would be to extract the main ideas and rationale behind the proposed methodology, to compare the approach the authors take with what we have discussed in class and to replicate as many of their results as possible.

  [added to list on 21 April]: `Bayesian Wavelet Analysis Using Nonlocal Priors with an Application to fMRI Analysis' by Nilotpal Sanyal and Marco A. R. Ferreira (2017), Sankhya B, Volume 79, Number 2, pp. 361-388. We discussed one version of Bayesian wavelet-based signal extraction in class that formulates a prior distribution for the wavelet coefficients one at a time. This paper considers a different Bayesian approach that couples wavelet coefficients together in an attempt to borrow strength from the clustering of coefficients locally and across scales (a `second generation' approach). A good project would be to compare the approach we discussed in class with the one proposed here and to attempt to replicated part of the authors' comprehensive simulation study in their Section 4.

  [added to list on 20 April]: `Seismic Trace Noise Reduction by Wavelets and Double Threshold Estimation' by Regis Nunes Vargas and Antonio Claudio Paschoarelli Veiga (2017), IET Signal Processing, Volume 11, Number 9, pp. 1069-1075. We discussed wavelet-based signal extraction in class that use different thresholding/shrinkage schemes. This paper proposes a variation of what we discussed in class to handle denoising of certain types of seismic time series. A good project would be to extract the main ideas, to contrast them to the schemes presented in Stat/EE 530 and to verify some of the computations that the authors present in support of the efficacy of their proposed methodology.

  [added to list on 20 April]: `Complex-Valued Wavelet Lifting and Applications' by Jean Hamilton, Matthew A. Nunes, Marina I. Knight and Piotr Fryzlewicz (2018), Technometrics, Volume 60, Number 1, pp. 48-60. The theory we have covered in Stat/EE 530 assumes that the time series is equally spaced. Lifting is a technique that was introduced in Sweldens (1996) and generalizes wavelet theory to apply for unequally sampled time series. Complex-valued wavelets offer some advantages over real-valued wavelets. This paper extends the notion of lifting to the complex-valued case. A good term project would be to mine out the key ideas in this paper, to contrast these ideas with wavelet theory for equally spaced data and to reproduce some of the computations in the article.

  [added to list on 18 April]: `Decorrelation Property of Discrete Wavelet Transform Under Fixed-Domain Asymptotics' by Xiaohui Chang and Michael L. Stein (2013), IEEE Transactions on Information Theory, Volume 59, Number 12, pp. 8001-8013. The asymptotic theory we have discussed in class for wavelet-based analysis of time series is based on letting the sample size get larger by increasing the length of time that the series is observed. Another alternative way to formulate asymptotic theory for time series is to let the sample size get larger by decreasing the sampling time between observations while fixing the length of time the series is observed. This paper looks into the decorrelation properties of the DWT using the alternative approach. A good term project would be to extract the key ideas in the papers and contrast them to what we have discussed in class.

  [added to list on 18 April]: `A Discrete Wavelet Spectrum Approach for Identifying Non-monotonic Trends in Hydroclimate Data' by Yan-Fang Sang, Fubao Sun, Vijay P. Singh, Ping Xie and Jian Sun (2018), Hydrology and Earth System Sciences, Volume 22, Number 1, pp. 757-766. This article considers the problem of testing for a non-monotonic trend in a time series using a wavelet-based approach. A good project would be to extract the key ideas in the paper and contrast them to the theory presented in class (in particular it would be interesting to compare the wavelet spectrum in their paper with the notion of wavelet variance discussed in Stat/EE 530). The authors apply their proposed methodology to simulated and actual time series. Verification of some of their results would be a good addition to the project.

  (spoken for by Clayton Barnes on 23 May): `How Much Information Does Dependence Between Wavelet Coefficients Contain?' by Carsten Jentsch and Claudia Kirch (2016), Journal of the American Statistical Association, Volume 111, Number 515, pp. 1330-1345. This article looks into the decorrelation properties of the discrete wavelet transform in considerably more detail than what was presented in Stat/EE 530. A good project would be to extract the key ideas in the paper and contrast them to the theory presented in class.

  [added to list on 16 April]: `Time-localized Wavelet Multiple Regression and Correlation' by Javier Fernandez-Macho (2018), Physica A - Statistical Mechanics and its Applications, Volume 492, pp. 1226-1238. This article looks into wavelet analysis of multiple time series and describes dynamics jointly shared by the series via a moving weighted regression of wavelet coefficients. A good project would be to extract the key ideas and to replicate as much as possible the author's analysis of Eurozone stock market time series.

  `Changes in the Variance of a Soil Property Along a Transect: A Comparison of a Non-stationary Linear Mixed Model and a Wavelet Transform' by R.M. Lark (2016), Geoderma, Volume 266, 15 March 2016, pp. 84-97.

  `Adjusting Wavelet-based Multiresolution Analysis Boundary Conditions for Long-term Streamflow Forecasting' by I. Maslova, A.M. Ticlavilca and M. McKee (2016), Hydrological Processes, Volume 30, Issue 1, pp. 57-74.

  `Wavelet Deconvolution With Noisy Eigenvalues' by Laurent Cavalier and Marc Raimondo (2007), IEEE Transactions on Signal Processing, Volume 55, Issue 6, Part 1, pp. 2414-2424.

  `On the Statistical Decorrelation of the Wavelet Packet Coefficients of a Band-limited Wide-sense Stationary Random Process' by Abdourrahmane Atto, Dominique Pastor and Alexandru Isar (2007), Signal Processing, Volume 87, Number 10, pp. 2320-2335.

  `Parametric Modelling of Thresholds across Scales in Wavelet Regression' by Anestis Antoniadis and Piotr Fryzlewicz (2006), Biometrika, Vol. 93, Number 2, pp. 465-471.

  (spoken for by Yufeng Bian on 25 May): `Wavelet Kernel Penalized Estimation for Non-equispaced Design Regression' by Umberto Amato, Anestis Antoniadis and Marianna Pensky (2006), Statistics and Computing, Volume 16, Number 1, pp. 37-55.