MM1: Time Series Analysis

Module title: Time Series Analysis (MM1)

Module convenor: Prof Sandra C. Chapman

Module aims:

This course will introduce the basic ideas underlying a broad range of modern time series analysis techniques in the context of physical processes and measurement constraints.

Learning objectives:

to be able to quantify properties of physical time-series and understand the impact of issues such as data gaps, non uniform sampling rate and experimental uncertainties.

As well as formal lectures this course will use tutorial material provided by Matlab (including Signal Processing and Wavelets toolboxes), and students are strongly encouraged to use Matlab for the assessed work.

Syllabus

Block 1: Fourier methods. Revision of Fourier theory and introduction to discrete Fourier transforms. Windowing, spectral estimates and spectral leakage. Methods for amplitude and phase spectra in ‘real’ signals- noise, nonuniform sampling in time and data gaps. Error estimates for power spectral density. Auto and cross correlation. [ LectureNotes-FTsummary.pdf LectureNotes-SpectralEstimates.pdf LectureNotes-Stationarity.pdf]

Block 2: General properties of transforms. Higher order spectra, Bicoherence, Tricoherence. Introduction to wavelets. . Wavelets to estimate spectral properties and as tools to decompose, detrend and denoise signals. Time stationarity and stochastic processes. Scaling. [ LectureNotes-GeneralizingFourier.pdf LectureNotes-Scaling.pdf LectureNotes_Wavelets.pdf LectureNotes_StructureFunctions.pdf]

Block 3: Higher Order Methods and nonlinear processes. Introduction to fractal and multifractal scaling. Methods to quantify scaling- Generalized Structure Functions and Probability Density Function collapse- relationship to Stochastic Differential Equation models. Dealing with finite size effects- uncertainties and outliers. Methods based on thresholding: Burst distributions and waiting times, delay plots. Mutual Information.

The module will be assessed with an extended worked example- students will be expected to apply a subset of the above ideas to a (provided) physical datasets and to write a short report on their results (see below).

Course texts:

  • Bracewell, The Fourier Transform and its Applications 2nd Ed McGraw Hill
  • Kantz and Schreiber, Nonlinear time series analysis, 2nd ed, CUP
  • Percival and Walden, Spectral analysis for physical applications, CUP
  • Percival and Walden, Wavelet methods for time series analysis, CUP
  • Sornette, Critical Phenomena, 2nd ed Springer
  • Sethna, Entropy, order parameters and complexity, OUP

Project and Assessment

To take part in this course for credit you will need to do the exercise in data analysis- this will be described in detail in the lectures. You will need to choose a timeseries to analyse from the RXTE websites:

The Readme files on RXTE Quicklook datafiles and the datasets are: RXTE ASM Lightcurves

For what is expected in the report see the file: Report.pdf

Reference material

Basic introduction to Fourier transforms and Matlab: basicFourierIntro.pdf and basicFouriermatlab.pdf

Matlab's own demos (both in Matlab and in the signal processing and wavelets toolboxes) are highly recommended.

Higher Order Spectra: ddw_review_hos_2003.pdf

Wavelets: torrence_compo_wavelets_1998.pdf , farge_wavelets_turb1996.pdf , farge_wavelets_turb2002.pdf

Observing power laws: clausetpowerlaws.pdf

Duration: 
2hs
Academic year: 
2010-2011
Starts: 
12/10/2010 - 15:00