Course Syllabus

Environmental Statistics II (MEES 708M)

Spring 2019


Slava Lyubchich

Dong Liang


Tuesday and Thursday, 3:30—5:00 p.m., IVN #800414

Course objective:

This course will extend statistical training of the students to advanced topics of time series analysis and spatial statistics. Aiming at the broad audience of students in the environmental sciences, we try to incorporate as many modern methods of analysis as possible. After taking this course, students will be familiar with a variety of state-of-the-art approaches for qualitative analysis of time- and space-dependent data. Moreover, students will become competent users of these methods by practicing them in class and in their homework assignments using the statistical programming language R.

Reference textbooks:

C&H: Chatterjee, S. and Hadi, A. S. 2006. Regression Analysis by Example. Wiley.

B&D: Brockwell, P.J. and Davis, R. A. 2002. Introduction to Time Series and Forecasting. 2nd ed. Springer, New York.

K&W: Kirchgässner, G. and Wolters, J. 2007. Introduction to Modern Time Series Analysis. Springer-Verlag, Berlin.

S&S: Shumway, R. H. and Stoffer, D. S. 2014. Time Series Analysis and Its Applications. With R Examples. EZ – 3rd Edition.

Bühlmann, P. 2002. Bootstraps for Time Series. Statistical Science: 17(1), 52–72.

W&G: Waller, L.A. and Gotway, C.A. 2004. Applied spatial statistics for public health data. Wiley.

ASDAR: Bivand, R.S., Pebesma, E. and Gomez-Rubio, V. 2013. Applied Spatial Data Analysis with R. Springer

W&O: Webster, R. and Oliver, M. A. 2007. Geostatistics for Environmental Scientists. 2nd ed. Wiley

B&G: Bailey, T. C. and Gatrell, A. C. 1995. Interactive Spatial Data Analysis. Longman

Grading and philosophy for the class:

Grades will be based on performance of two take home exams, an individual project, and homework problem sets. Each exam and individual project will represent 30% of the grade. The homework problem sets will make up the remaining 10%. In cases when students are at the borderline between lower and higher grades, a high level of participation in the class discussions and class in general will win the day for the higher grade.

Homework problems are essential to understand the materials. Although the homework comprises only 10% of the final grade, performance on the exams is usually correlated with effort on the homework problems. Whereas plagiarism will not be tolerated, students are encouraged to work together to learn from one another and solve homework problems in a collaborative and collegial way (aside from the take home exam).

Distribution of class materials:

We will use the distance learning tool, Moodle (, to store and disseminate class information: class notes, R code and output, assigned readings, and even discussion threads. Each student will be given a personal login and password to access the site. You are encouraged to download and bring the materials to the lectures.

Spring 2019 academic calendar:

First Day of Classes January 29

Spring Break March 17-24

Midterm 1 deadline March 28

Final Project May 10

Last Day of Classes May 14

Reading Day May 15

Midterm 2 deadline May 23

Copyright notice:

Lectures and course materials, including power point presentations, tests, outlines, and similar materials, are protected by copyright. The instructor is the exclusive owner of copyright in those materials he creates. You may take notes and make copies of course materials for your own use. You may not and may not allow others to reproduce or distribute lecture notes and course materials publicly whether or not a fee is charged without instructor's written consent. Similarly, you own copyright in your original papers and exam essays. If instructor is interested in posting your answers or papers on the course web site, he will ask for your written permission.

Persons who publicly distribute or display or help others publicly distribute or display copies or modified copies of an instructor's course materials may be considered in violation of the University Code of Student Conduct, Part 9(k).

Tentative course calendar:





1. Review of multiple linear regression, Gauss-Markov theorem. Model assumptions and diagnostics (parametric and non-parametric).

C&H Ch. 3-4


2. Remedial approaches: transformation of variables, weighted least squares. Introduction to errors serially correlated in time or space.

C&H Ch. 6-9


3. Time series and its components (trend, cycles, seasonality, noise). Autocorrelation function. Smoothing. Trend- and difference-stationary time series.

B&D Ch. 1


4. Stationary time series: AR, MA, ARMA.

B&D Ch. 2, 3, 5



B&D Ch. 6


6. ARCH and GARCH.

K&W Ch. 7


7. Parametric and non-parametric methods for trend detection (Wilcoxon, Sen’s slope, WAVK, unit-root test). Bootstrap.

B&D Ch.1.6, notes, Buhlmann (2002)


8. Time series synchronism and clustering.



9. Granger causality.

K&W Ch. 3


10. Cointegration.

K&W Ch. 6


11. Regression with correlated errors (ARMAX), with seasonality (dummy variables, trigonometric regressors).

S&S Ch. 5.5-5.7


12. Spectral decomposition.

S&S Ch. 4


13. Dynamic Fourier analysis and wavelets.

S&S Ch. 4


14. Model diagnostics and forecasting.

B&D Ch. 9

Spring break


15. Mixed effect model for nested data

Zurr Ch 5


16. Generalized linear model for discrete data

Zurr Ch 8-10


17. Geostatistical process and variogram

Ch. 3-6 W&O


18. Local estimation or Kriging

Ch. 8 W&O


19. Corss-Correlation, Coregionalization and Cokriging

Ch. 10 W&O


20. Spatial ANOVA

Ch. 12 W&O


21. Spatial point processes, estimation

Ch. 5 W&G


22. Spatial clusters of health events

Ch. 6 W&G


23. Area, Raster and Network data, EDA

R:Raster Ch. 7.4 W&G


24. Cluster and clustering

Ch. 7.3, 7.5 W&G


25. Spatial autoregressive models

Ch. 9.3 W&G


26. Generalized linear spatial models

Ch. 9.4 W&G


27. Large spatial data modeling



Class presentations


Class presentations

Individual project on time series or spatial data analysis*

  1. Decide on a series of questions of interest and the associated hypotheses and predictions that you will attempt to test and answer with inferential statistics covered in class.

  2. Design an experiment/study or analysis (if using an existing dataset) to answer these questions.

  3. Identify and obtain or generate a dataset to analyze.

  4. Analyze the data and prepare a report as you would for the scientific journal ‘Ecology’. Include in the Discussion a section on how you might better design the study/experiment if you had the opportunity to do things over again.

    Report limited to 10 double spaced pages of text (including literature cited) with 1” margins and 12 pt font. Title page, tables, and figures are in addition to the page limit. Be concise yet informative, organized, and well written.

    The last days of classes will be reserved for project presentations. Everyone will have a chance to present their project findings in the standard (10-15 minutes talk, including questions). Exact time for each presentation will depend on the total enrollment and will be determined during the course. This should be a good exposure to giving talks at scientific meetings. The time limit will be rigidly enforced.

*Well done projects are sometimes good enough to publish or may become a chapter in your thesis, so keep this in mind during your project.