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Time Series Analysis

Course in Climate Time Series Analysis

Over 40 courses have already been taught. Below description is for offline courses taught here at our site in Germany. With regard to online format, please see the announcements in the internet or contact us.

Five-day course, given by Dr. Manfred Mudelsee and based on his book. Consists of lectures and computer tutorials.

Course is in English. Assumed level is post-graduate or post-doctoral. A basic knowledge in statistics is required. For example, you should have an idea what "standard deviation" means. After the course, your knowledge shall be deeper.

Course is limited to 8 participants maximum. This allows us to give you individual feedback during the tutorials. You are very welcome to bring your own data for analysis.

Bring your laptop with you! You get all course material in electronic form (PDF, Windows executables, Fortran source codes), and you get a printed copy of the book.

Either check for a specific, offered course on this website, or contact CRA for your individual course proposal and pricing. Here is the contact form.

  • Climatologists
  • Ecologists
  • Environmental researchers
  • Geographers
  • Geologists
  • Hydrologists
  • Meteorologists
  • Physicists
  • Risk analysts
  • Statisticians
Typical time schedule
Day 1: Introduction
  • Climate archives
  • Timescales
  • Fundamental concepts of time series analysis
Day 1: Persistence models
  • Stochastic processes
  • Short versus long memory
Day 2: Bootstrap confidence intervals
  • Statistical estimation
  • Standard errors, bias, confidence intervals
  • Classical methods
  • Bootstrap resampling
  • Monte Carlo methods
  • Hypothesis tests
Day 2: Regression I
  • Linear regression
  • Nonlinear regression
  • Nonparametric regression or smoothing
  • Example: climate transitions
Day 3: Spectral Analysis
  • Spectrum and periodogram
  • Multitaper estimation
  • Lomb–Scargle periodogram
  • Example: solar cycles
Day 3: Extreme value time series
  • Data types and risk estimation
  • Stationary models (GEV, GP)
  • Nonstationary models (Poisson)
  • Example: flood risk analysis
  • Example: hurricane risk
Day 4: Correlation
  • Pearson's correlation coefficient
  • Spearman's rank correlation coefficient
  • Example: runoff variations
Day 4: Regression II/Open Session I (Re-Cap, More Applications, More Theory, In-Depth Analyses, Individual Consultations, etc.)
  • Errors-in-variables model
  • Prediction
  • Example: climate sensitivity
  • Example: proxy calibration
Day 5: Future directions/Open Session II
  • Timescale modelling
  • Higher dimensions
  • Climate models
  • Optimal estimation
Climate-related computer tutorial exercises (selection)
  • Quantification of the Northern Hemisphere Glaciation in the Pliocene by means of change-point regression
  • Comparing climate-model simulated runoff in different scenarios
  • Nonparametric trends in regional Holocene climate with bootstrap confidence band
  • Sunspot spectrum estimation
  • Hurricane activity over the past 1000 years examined with nonstationary risk analysis
  • Correlations between measured river runoff series from different hydrological stations
  • Calibration of a paleoclimatic proxy variable