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Introduction to Time Series Analysis

Time series analysis is a very complex topic, far beyond what could be covered in this class. Hence the goal of the class is to give a brief overview of the basics in time series analysis. Further reading is therefore recommended.
  • The PDF of the course is here
  • 0. Test your environnement:
    • Dear honors student 2021, Due to the COVID19 crisis, the "ocean stats" class will be taught remotely. We will use Zoom and Whatsapp to communicate. I will broadcast a powerpoint presentation and you will do some practicals using Matlab. Don't worry, the class is not about writing Matlab scripts, but primarily about statistics. However, each of you needs to be able to run Matlab and open NetCDF files. Below is a small NetCDF file and a simple Matlab script. Can you please download both files, open Matlab and run the script. Please, let the Honors'rep know if you encountered problems or if everything is fine.
  • 1. Introduction to Times Series:

  • 2. Descriptive Satistics:
    • Course Time Series 2: Descriptive Satistics
      • Sampling and Aliasing
      • Histograms and Density curves
      • Statistical Moments: mean, variance, skewness, kurtosis; median, mode
      • Quantiles and box plot
      • Notion of Stationarity
    • Practical 2 with Solutions:

  • 3. Distributions and Statistical Tests:
    • Course Time Series 3: Distributions and Statistical Tests
    • Course Time Series 3: Statistical tables (Go here)
      • Theoretical statistical distributions (Uniform, Normal, Chi-square, Student, Fisher ...)
      • Inferential statistics
      • Test if the distribution is normal
      • Test the difference in mean of two samples
      • Test the difference in variance of two samples
    • Practical 3 and Solutions:
    • Article by Prigent et al (2020): Origin of Weakened Interannual Sea Surface TemperatureVariability in the Southeastern Tropical Atlantic Ocean (GRL) (Prigent et al., 2020)

  • 4. Comparison of data:
    • Course Time Series 4: Comparison of data
      • Interpolation and regridding
      • Normalization
      • Scatter-plot, binned scatter plot
      • Covariance and Pearson Correlation
      • Taylor diagram
      • Spatial correlation
      • Independence, degrees of freedom and risk accumulation
      • Linear regression (least square method)
      • Quantile-Quantile plot
      • Partial correlation
    • Practical 4_1 and Solutions:
    • Practical 4_2 and Solutions:
    • Article presenting the Taylor diagram: Summarizing multiple aspects of model performance in a single diagram, by Karl E. Taylor, JGR 2001 (Taylor et al., 2001)

  • 5. Time Frequency Analyses:

  • 6. Spatio-Temporal Analyses: