This page contains all online information relevant for the module, including various data files you will need to complete the assignments as well as links to online resources which might be useful.

Notes and hand-outs

• course notes, updated regularly: notes_CO907.pdf (preliminary final version updated 2.12., please let me know about typos and errors)
  2.12.: added viva questions and small formatting (CLT and LLT) and typo correction in Section 1.
  
• separate file for possible viva_questions.pdf (this is NOT and exclusive list of questions, but covers all topics)
  
  
• handout1.pdf (characteristic functions, Gaussians, LLN, CLT)
  
• MATLAB Tips (by Tom Nichols)
  
• MATLAB_commands.pdf (by Jiarui Cao)
  

Problem sheet 1

• sheet1.pdf (graphical analysis, characteristic functions, correlations, Bayes' rule, MLE, CLT and extreme value statistics, entropy)
  
• files for Q1.1: data11.dat, data12.dat, data13.dat
  
• files for Q1.3 and Q1.5: Midlandstemperatures.zip (data from the Metoffice website)
  
• file for Q1.6: exponential.dat
  

Problem sheet 2

• sheet2.pdf (curve fitting, model selection, autoregressive models, extracting signal from noise, spectral analysis, smoothing and filtering)
  
• files for Q2.4: ftse.dat, xray.dat, temperatureanomaly.dat
  
• files for Q2.1, Q2.3, Q2.7: curvefitting2013.dat, signalinnoise.dat, sunspots,dat
  
• to actually test a timeseries for stationarity you can use a uni root test (NOT required for the homework)
  

Files from classes

• Class 1: CDF_Tail.m, LawofLargeNum.m, LoadData_BoxPlot.m, QQPlots.m
  temperature data file: daily-maximum-temperatures-in-me.xls
• Class 2: Q1_5a.m, Q1_7a.m, Q1_7b.m, Q1_7bnew.m (does the scaling for different n)
  
• Class 5: Q2_4.m, Q2_4_new.m, Q2_5a.m, Q2_5b.m, Q2_5c.m, Q2_6.m, Q2_7a.m
  
• detrended_data.zip (UPDATED ON 3.12.! OK if you have already used old version for homework. Contains: FTSE, xray, temperature anomaly)
  
• thanks a lot to Elena, Michael and Alex to make their homework files available, which are in general very nice. Klick here to download.
  some specific comments:
  
  1. Q2.1(c) stationary processes can have covariance functions that do not decay quickly, the confidence intervals are just there to indicate when the correlations are indistinguishable from iid noise. One way to check for stationarity is to plot the AC function starting at different times (see Elena's solution page 3 and 5, I think both show relatively good collapse for the ACs the not-detrended series should look much worse).
     
  2. general: when presenting plots it is often good to show several versions with different zoom etc, I think this is very well done in Michael's and Alex' solution
     
  3. Q2.2(d) different realizations of AR(q) models with the same parameter values are not expected to overlap at all since they are random processes (even if they coincide at the initial conditions).
     

Online resources

• on this wikipedia page you can listen to and read about different kinds of noise.
  
• Online Time Series Data Library - contains lots of useful examples from a huge variety of applications.
• M. E. J. Newman, "Power laws, Pareto distributions and Zipf's law." Contemporary Physics 46, 323 (2005).
• A. Broder et al., "Graph structure in the Web." Computer Networks 33, 309 (2000).
• A. Clauset, C.R. Shalizi, and M.E.J. Newman, "Power-law distributions in empirical data" SIAM Review 51(4), 661-703 (2009). (arXiv:0706.1062, doi:10.1137/070710111)