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 simulation study;
• methodological or theoretical research;
• a critical review of the literature on one of the many aspects of time series analysis that we won't be covering fully in class;
• some combination of the above; or
• any idea that you come up with that will help you learn more about time series analysis.

• 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 519. Thus, while it is fine to refer to, say, a `Gaussian ARMA process' 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 commonly used 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 one of the the class textbooks or as a potential submission to a journal. For clarity, you might try to adopt the notation and terminology of the class overheads 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 time series 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 (computer simulations), 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, make sure that you give enough information so that others could reproduce your results if they so desired. For example, if you do a simulation study that depends on some parameter values, make sure you indicate how these values were set.
• After making comments on your written report, I will scan it and email the scan to you sometime after the quarter is over.

  [spoken for by Jianshun Wu on 26 February]: Elena Barton, Basad Al-Sarray, Stephane Chretien and Kavya Jagan (2018), `Decomposition of Dynamical Signals into Jumps, Oscillatory Patterns, and Possible Outliers,' Mathematics, 6(124), 13 pages. The classical decomposition model we discussed in class breaks up a time series into three components, namely, a trend, a periodic component and a mean-zero stationary process (see overheads III-10, III-11 and III-19). This article breaks up a time series into three components also, but quite different ones. The proposed decomposition makes use in part of l1 trend filtering that we briefly discussed in class (see overheads III-59 to III-68). An interesting project would be to extract the main ideas in this article, to compare them to what we discussed in class and, if possible, to apply the proposed methodology to some of the time series we have discussed (or to other series that might be of interest).

  [added to list on 31 Jan]: Hajo Holzmann, Axel Munk, Max Suster and Walter Zucchini (2006), `Hidden Markov Models for Circular and Linear-Circular Time Series,' Environmental and Ecological Statistics, 13, pp. 325-347. The analysis of a time series of directional data (e.g., wind directions) presents challenges not easily addressed by, e.g., ARMA models. This article proposes an approach based on hidden Markov models and constrasts this approach with others that have been proposed in the literature. There is more than enough material here to make for the basis of a good term project if directional data is of interest to you.

  [added to list on 16 Jan]: Hiroshi Yamada (2018), `A New Method for Specifying the Tuning Parameter of l1 Trend Filtering,' Studies in Nonlinear Dynamics & Econometrics, 22(4), 20160073, 8 pages. We discussed l1 trend filtering briefly in class (see overheads III-59 to III-68), but did not address the issue of how to set the tuning parameter lambda. This paper addresses this issue. An interesting term project would be to mine out and critique the key ideas. Are there any other methods around that would be viable competitors to what is advocated here?

  [added to list on 15 Jan]: Pramita Bagchi, Moulinath Banerjee and Stilian A. Stoev (2016), `Inference for Monotone Functions Under Short- and Long-Range Dependence: Confidence Intervals and New Universal Limits,' Journal of the American Statistical Association, 111(516), pp. 1634-1647. This paper considers point-wise confidence intervals for a trend described by a monotone function observed in the presence of additive noise, which is a stationary process with either short-range dependence (e.g., an ARMA process) or long-range dependence (e.g., a fractionally differenced process). In addition to extracting and critiquing the key ideas, a good term project would include reproduction of some of the simulations and data analysis reported in the paper.

  [added to list on 15 Jan]: Mayer Alvo and Paul Cabilio (1994), `Rank Test of Trend When Data Are Incomplete,' Environmetrics, 5(1), pp. 21-27, along with Paul Cabilio and Jessica Tilley (1999), `Power Calculations for Tests of Trend with Missing Observations,' JOURNAL, 10(6), pp. 803-816. Both of these articles tackle the problem of testing for trend for time series with missing observations (i.e., gappy series). The proposed methodology makes use in part with rank statistics, which we are touched in Stat 519. There is quite a bit of material here for a term project: extraction and critique of the key ideas and replication of simulations and of analysis of actual time series.

  [added to list on 15 Jan]: Thomas J. Fisher and Michael W. Robbins (2018), `An Improved Measure for Lack of Fit in Time Series Models,' Statistica Sinica, 29(3), pp. 1285-1305. The paper describes an alternative to the portmanteau test for goodness of fit we talked about in class. A good term project would be to figure out and critique their improvement upon the portmanteau test; to do the same for alternatives they propose; and replicate some of their simulation studies.

  [added to list on 15 Jan]: Karolos K. Korkas and Piotr Fryzlewicz (2017), `Multiple Change-Point Detection for Non-Stationary Time Series using Wild Binary Segmentation,' Statistica Sinica, 27(1), pp. 287-311. Here is another take on detecting changes in a time series. The proposed methodology allows for estimation of both the number and locations of changes in the second-order structure of a time series. The methodology is implemented in the R package wbsts (available from CRAN using the R command `install.packages("wbsts")'). A good term project would be to extract and critique the key ideas and to replicate part of the simulations described by the authors (their Models A to I all involve processes studied in Stat 519).

  [added to list on 11 Jan]: Claudia Kirch and Joseph Tadjuidje Kamgaing (2015), `On the Use of Estimating Functions in Monitoring Time Series for Change Points,' Journal of Statistical Planning and Inference, 161, pp. 25-49. A classic problem in time series analysis is detecting a change of some sort in a time series as time progresses. This paper makes use of so-called estimating functions to do so. A good term project would be to mine out and critique the key ideas in this paper and to replicate part of the simulations that the authors used to study their methodology (or to replicate one or more of their examples using actual time series). There are many other approaches to monitoring change points, some of which are described in papers referenced by this paper - these could also provide the starting point for a good term project.

  [added to list on 11 Jan]: Jonathan Hill, Deyuan Li and Liang Peng (2016), `Uniform Interval Estimation for an AR(1) Process with AR Errors,' Statistica Sinica, 26(1), pp. 1649-1672. Subtle issues arise in estimating the parameter phi in the AR(1) model when phi is close to unity (unit root tests are related to these issues). This paper looks into a scheme for getting estimates of phi that work the same whether phi is close to unity or not. An interesting aspect of this paper is the use of AR errors to drive an AR(1) process. A good term project would be to extract and critique the key ideas.

  [spoken for by Yun Xie on 21 February]: Antonio E. Noriega and Daniel Ventosa-Santaularia (2006), `Spurious Regression Under Broken-Trend Stationarity,' Journal of Time Series Analysis, 27(5), pp. 671-684. This article could be used as a starting point for looking into the phenomenon of spurious regression, which has been addressed in a number of articles, including those referenced in the authors' introduction (this article is fairly old, and undoubtedly there have been a lot more articles about the subject since 2006). A good term project would be to review the key ideas and offer critiques of the various approaches to the subject.

  [added to list on 11 Jan]: Song Xi Chen, Lihua Lei and Yundong Tu (2016), `Functional Coefficient Moving Average Model with Applications to Forecasting Chinese CPI,' Statistica Sinica, 26(4), pp. 1649-1672. This article investigates allowing the coefficient in an MA(1) model to adapt to a covariate with application to CPI data from China and to German egg prices. A good term project would be to extract the key ideas and to replicate either some of the authors' simulation studies or their analyses of the CPI and egg price time series (it is not clear if either of these series are readily available).

  [added to list on 11 Jan]: Timothy J. Vogelsang and Nasreen Nawaz (2017), `Estimation and Inference of Linear Trend Slope Ratios With an Application to Global Temperature Data,' Journal of Time Series Analysis, 38(5), pp. 640-667. This article looks at the problem of estimating the ratio of linear trend slopes for two time series (motivated in part by two climate time series, one related to warming rate in the lower troposphere, and the other, to the rate at the earth's surface). A good term project would be to extract the key ideas behind the proposed estimator and also to try to reproduce some the extensive simulations the authors carried out to study the efficacy of their estimator.

  [added to list on 15 Nov]: Kun Chang, Rong Chen and Thomas B. Fomby (2017), `Prediction-based Adaptive Compositional Model for Seasonal Time Series Analysis,' Journal of Forecasting, 36(7), pp. 842-853. This article presents what appears to be an interesting twist on modeling seasonal time series. A good project would be to mine out the key ideas, compare them to what we have discussed in class and replicate some of the computer experiments conducted by the authors.

  [added to list on 7 Nov]: Y. Zhang, P. Cabilio and K. Nadeem (2016), `Improved Seasonal Mann-Kendall Tests for Trend Analysis in Water Resources Time Series'; pp. 215-229 in `Advances in Time Series Methods and Applications: the A. Ian McLeod Festschrift', Springer (edited by W.K. Li, D.A. Stanford and H. Yu). This article considers a way of assessing the significance of a trend in the classical decomposition model in which a time series is the sum of a possible trend, seasonal variations and a stationary process. A nice project would be to extract the basic ideas behind the Mann-Kendall test, to replicate the simulation study carried out in the paper and to apply it to one or more of the time series we have looked at (the accidental death series would be a good candidate).

  [added to list on 7 Nov]: An investigation into the basic ideas behind functional time series analysis and in particular the functional AR(1) model (FAR(1) model) should make for an interesting project. Information about the FAR(1) model is available on the internet, but there is also a short introduction to the subject in Section 8.2 of the book Introduction to Functional Data Analysis by P. Kokoszka and M. Reimherr (CRC Press, 2017). The UW library does not currently have this book, but I have a personal copy (talk to me if this topic is of interest to you).

  [added to list on 7 Nov]: D. Pena and J. Rodriguez (2002), `A Powerful Portmanteau Test of Lack of Fit for Time Series,' Journal of the American Statistical Association, 97, No. 458, pp. 601-610. A good project would be to compare the test proposed here with the portmanteau test we discussed in class (starting with overhead IV-8).

  [added to list on 7 Nov]: Xiaofeng Shao (2015), `Self-Normalization for Time Series: A Review of Recent Developments,' Journal of the American Statistical Association, 110, No. 512, pp. 1797-1817. This paper covers a wealth of material. A good project would be to focus on ideas in the paper concerning construction of a confidence interval for the mean of a stationary process and to compare these ideas to what we discussed in class (starting with overhead V-6).