Time Series Analysis
about
Welcome to Time Series Analysis for Environmental Sciences (71606) at the Hebrew University of Jerusalem. This is Yair Mau, your host for today. I am a senior lecturer at the Institute of Environmental Sciences, at the Faculty of Agriculture, Food and Environment, in Rehovot, Israel.
This website contains (almost) all the material you’ll need for the course. If you find any mistakes, or have any comments, please email me.
disclaimer
does not constitute a stand alone course in Time Series Analysis. This is only the support material for the actual presential course I give.
what, who, when and where?
syllabus
course description
Data analysis of time series, with practical examples from environmental sciences.
course aims
This course aims at giving the students a broad overview of the main steps involved in the analysis of time series: data management, data wrangling, visualization, analysis, and forecast. The course will provide a hands-on approach, where students will actively engage with real-life datasets from the field of environmental science.
learning outcomes
On successful completion of this module,students should be able to:
- Explore a time-series dataset, while formulating interesting questions.
- Choose the appropriate tools to attack the problem and answer the questions.
- Communicate their findings and the methods they used to achieve them, using graphs, statistics, text, and a well-documented code.
course content
- Data wrangling: organization, cleaning, merging, filling gaps, excluding outliers, smoothing, resampling.
- Visualization: best practices for graph making using leading python libraries.
- Analysis: stationarity, seasonality, (auto)correlations, lags, derivatives, spectral analysis.
- Forecast: ARIMA
- Data management: how to plan ahead and best organize large quantities of data. If there is enough time, we will build a simple time-series database.
books and other sources
course evaluation
There will be 2 projects during the semester (each worth 25% of the final grade), and one final project (50%).
weekly program
week 1
- Lecture: Course overview, setting of expectations. Introduction, basic concepts, continuous vs discrete time series, sampling, aliasing
- Exercise: Loading csv file into python, basic time series manipulation with pandas and plotting
week 2
- Lecture: Filling gaps, removing outliers
- Exercise: Practice the same topics learned during the lecture. Data: air temperature and relative humidity
week 3
- Lecture: Interpolation, resampling, binning statistics
- Exercise: Practice the same topics learned during the lecture. Data: air temperature and relative humidity, precipitation
week 4
- Lecture: Time series plotting: best practices. Dos and don’ts and maybes
- Exercise: Practice with Seaborn, Plotly, Pandas, Matplotlib
Basic data wrangling, using real data (temperature, relative humidity, precipitation) downloaded from USGS. 25% of the final grade
week 5
- Lecture: Smoothing, running averages, convolution
- Exercise: Practice the same topics learned during the lecture. Data: sap flow, evapotranspiration
week 6
- Lecture: Strong and weak stationarity, stochastic processes, auto-correlation
- Exercise: Practice the same topics learned during the lecture. Data: temperature and wind speed
week 7
- Lecture: Correlation between signals. Pearson correlation, time-lagged cross-correlations, dynamic time warping
- Exercise: Practice the same topics learned during the lecture. Data: temperature, solar radiation, relative humidity, soil moisture, evapotranspiration
week 8
Same as lecture 7 above
week 9
- Lecture: Download data from repositories, using API, merging, documentation
- Exercise: Download data from USGS, NOAA, Fluxnet, Israel Meteorological Service
Students will study a Fluxnet site of their choosing. How do gas fluxes (CO2, H2O) depend on environmental conditions? 25% of the final grade
week 10
- Lecture: Fourier decomposition, filtering, Nyquist–Shannon sampling theorem
- Exercise: Practice the same topics learned during the lecture. Data: dendrometer data
week 11
- Lecture: Seasonality, seasonal decomposition (trend, seasonal, residue), Hilbert transform
- Exercise: Practice the same topics learned during the lecture. Data: monthly atmospheric CO2 concentration, hourly air temperature
week 12
- Lecture: Derivatives, differencing
- Exercise: Practice the same topics learned during the lecture. Data: dendrometer data
week 13
- Lecture: Forecasting. ARIMA
- Exercise: Practice the same topics learned during the lecture. Data: vegetation variables (sap flow, ET, DBH, etc)
Final Project
In consultation with the lecturer, students will ask a specific scientific question about a site of their choosing (from NOAA, USGS, Fluxnet), and answer it using the tools learned during the semester. The report will be written in Jupyter Notebook, combining in one document all the calculations, documentation, figures, analysis, and discussion. 50% of the final grade.