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Matematikcentrum

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Stationary Stochastic Processes

News HT 2018

The course is concluded with a written exam, Friday November 2, 14.00-19.00, at Victoriastadion, Vic:2 and 3A.

The exam will be in english. You are allowed to bring a pocket calculator and the table of formulas of this course. You can also bring some small 'high school' table of formulas in mathematics (e.g. TEFYMA). Table of formulas must not contain any marks or comments.

 

Additional Question Times for the Exam

Wed Oct 24 10.15-12.00 MH:227. 

Tue Oct 30 10.15-12.00 MH:227. 

Thu Nov 1 10.15-12.00 MH:227. 

 

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The  registration system opens for Computer exercise 3, October 8.00. Register here.

Answer the questions in 1.1 of the tutorial of Comp. exercise 3 and E-mail your answers to FMSF10@matstat.lu.se at latest by Thursday morning October 11 at 8.00 

An updated folder with the extra files for the exercises are found here.

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The  registration system opens for Computer exercise 2, September 25 8.00. Register here.

Answer the questions in 1.1 of the tutorial of Comp. exercise 2 and E-mail your answers to FMSF10@matstat.lu.se at latest by Friday morning September 28 at 8.00.

Please find information on advanced courses in Mathematical Statistics here

In case of illness where you are not able to attend your scheduled computer exercise, you should immediately contact the computer exercise coordinator, see E-mail adress to the right. 

The three computer exercises are mandatory and the registration system opens for Comp. exercise 1: September 11 8.00. Register here.

Answer the questions in 1.1 of the tutorial of Comp. exercise 1  and E-mail your answers to FMSF10@matstat.lu.se at latest by Friday morning September 14 at 8.00. The answers can be written in english or swedish by hand (readable) or in any text editor program but the final attached file should be a pdf-file. Use the following in the subject row, "Assignment 1 by tpi07xyz" (one student) or  "Assignment 1 by tfy08xyz and nat09xyz" (two students). 

The computer exercises require basic knowledge of Matlab. If you have not used Matlab, prepare by writing simple command lines and collect them in a script. The extra files for the exercises are found here.

 

 

Course contents

Stochastic processes find applications in a wide variety of fields and offer a refined and powerful framework to examine and analyse time series. This course presents the basics for the treatment of stochastic signals and time series. For a stochastic process to be stationary, the mechanism of the generation of the data should not change with time. Mathematical tools for processing of such data is covariance and spectral analysis, where different models could be used.  Some usual models are autoregressive (AR) and moving average (MA) processes. For appropriate modelling, we need reliable estimation of covariance functions and spectral densities.  Linear filtering, differentiation and integration of stationary stochastic processes are other important parts of this course. 

Schedule

Lectures (2 times a week) 

Lectures, covering the different chapters of the course are given Mondays 13.15-15.00 and Tuesdays 10.15-12.00 in MH:Riesz.  

 

Lectures with preliminary schedule

  1. Mon Sept 3 13.15-15.00 Lecture 1, Ch. (1), 2.1, 2.2.1, 2.3.2, 2.5.2, 2.2.2
  2. Tue Sept 4 10.15-12.00 Lecture 2, Ch. 2.3.3, 2.3.1, 2.2.3, 2.5.1, (2.5.3), (2.6)
  3. Mon Sept 10 13.15-15.00 Lecture 3, Ch. 5.1, 5.2, 2.4, 4.1, 4.2, (4.3.2) 
  4. Tue Sept 11 10.15-12.00 Lecture 4, Ch. 4.2, 4.3.1, 9.3
  5. Mon Sept 17 13.15-15.00 Lecture 5, Ch. 4.4, (4.5.1)  
  6. Tue Sept 18 10.15-12.00 Lecture 6, Ch. 9.1, 9.2, 9.4, 9.5.2, (9.5.3)
  7. Mon Sept 24 13.15-15.00 Lecture 7, (the error in page 14 is now updated)  Ch. 6.1, 6.2 
  8. Tue Sept 25 10.15-12.00 Lecture 8, Ch. (6.3.1), 6.3.2, (6.4), 6.5, 9.5.4
  9. Mon Oct 1 13.15-15.00 Lecture 9, Ch. 7.1, 7.2, (7.3)
  10. Tue Oct 2 10.15-12.00 Lecture 10, (some errors are corrected) Ch.  8.4, 8.5
  11. Mon Oct 8 13.15-15.00 Summary and old exam exercises

 

Weekly Exercise schedule

The exercises are found in the course book and and the solution manual is included below under 'Course material'. The extra exercises numbered with X1, X2 …  with solutions are found in the Xtra exercises below together with a useful table of formulas. The exercises are marked with three levels: (-1) if you have forgot some of the prior knowledge or need extra training, (0) should be computed by everyone, (+1) if you are fast and want highest grade of the exam.    


  1. Week 1: (September 3 - September 7) 2.1(-1), 2.2(-1), 2.3(0), 2.4(+1), 2.6(0), 2.8(0), 2.9(0), 2.10(+1), 2.11(0), 2.12(0), 2.13(+1), 2.14(0), 2.15(0), 2.16(+1), 2.18(0). Example1.pdf, Example1-with-sound.mp4, Example2.pdfExample2-with-sound.mp4
  2. Week 2: (September 10 - September 14) 5.1(0), 5.2(0), 4.1(-1), 4.2(0), 5.3(+1), 4.3(0), 4.4(0), 4.5(0), 4.6(0), 4.7(0), X1(0), X2(0), X3(-1), 4.9(+1). Example5.pdf, Example3.pdf, Example3-with-sound.mp4 
  3. Week 3: (September 17 - September 21) 4.10(0), 4.11(0), X4(0), X5(+1), X6(0), X7(+1), 9.1(+1), 9.2(+1), 9.3(0), X8(0), X9(0), 9.4(+1), 9.5(0), X10(0). Example4.pdfExample4-with-sound.mp4  
  4. Week 4: (September 24 - September 28) ): X11(-1), X12(0), 6.1(0), 6.2(0), 6.3(0), 6.4(+1),  X13(0), X14(+1), 6.7(-1), 6.8(-1), X15(0), X16(0), X17(+1), 6.9(0), 6.10(0), X18(+1). Example6.pdf 
  5. Week 5: (October 1 - October 5) 7.1(0), 7.2(-1), X19(0), X20(0), X21(0), 7.4(+1), 7.5(+1), 7.6(0), X22(-1), X23(0), 7.7(0), 7.8(-1), X24(0), X25(0), 7.9(+1), 7.10(+1), 7.13(+1). Example7.pdf, Example8.pdf
  6. Week 6: (October 8 - October 12) X26(0), X27(0), X28(+1), X29(0), 8.9(0), X30(+1), 8.2(0), 8.3(0), 8.4(+1), 8.5(0), X31(0), 8.7(+1), X32(+1).       
  7. Week 7: (October 15 – October 19) Review and old exams, see below.

Question Times 

  • Thu Sept 6 8.15-10.00, MH:229: Thu Sept 6 13.15-15.00, MH:227: Fri Sept 7 13.15-15.00, MH:229.
  • Thu Sept 13 8.15-10.00, MH:229: Thu Sept 13 13.15-15.00, MH:227: Fri Sept 14 13.15-15.00, MH:229.
  • Thu Sept 20 8.15-10.00, MH:229: Thu Sept 20 13.15-15.00, MH:227: Fri Sept 21 13.15-15.00, MH:229.
  • Thu Sept 27 8.15-10.00, MH:229: Thu Sept 27 13.15-15.00, MH:227: Fri Sept 28 13.15-15.00, MH:229.
  • Thu Oct 4 8.15-10.00, MH:229: Thu Oct 4 13.15-15.00, MH:227: Fri Oct 5 13.15-15.00, MH:229.
  • Thu Oct 11 8.15-10.00, MH:229: Thu Oct 11 13.15-15.00, MH:227: Fri Oct 12 13.15-15.00, MH:229.
  • Thu Oct 18 8.15-10.00, MH:229: Thu Oct 18 13.15-15.00, MH:227: Fri Oct 19 13.15-15.00, MH:229.

 

Additional Question Times for the Exam

Wed Oct 24 10.15-12.00 MH:227. 

Tue Oct 30 10.15-12.00 MH:227. 

Thu Nov 1 10.15-12.00 MH:227. 

 

Computer exercises (3 occasions) - Mandatory

The computer exercise tutorials should be studied and preparations should be computed, answered and uploaded before you come to the exercise! The exercises use Matlab and additional m-files and data. The extra files are found here. Please load when starting the exercise.

Comp. exercise 1:

  • Tue Sept 18 13.15-15.00 (E:Hacke, E:Panter, E:Val)
  • Wed Sept 19 10.15-12.00 (E:Satu, E:Uran)  
  • Fri Sept 21 15.15-17.00 (E:Elg, E:Elgkalv)

Comp. exercise 2:

  • Tue Oct 2 13.15-15.00 (E:Hacke, E:Panter, E:Val)
  • Wed Oct 3 10.15-12.00 (E:Satu, E:Uran)
  • Fri Oct 5 15.15-17.00 (E:Elg, E:Elgkalv)

Comp. exercise 3:

  • Mon Oct 15 13.15-15.00 (E:Satu, E:Uran)
  • Tue Oct 16 13.15-15.00 (E:Hacke, E:Panter, E:Val)
  • Fri Oct 19 15.15-17.00 (E:Elg, E:Elgkalv)

Course material

The course book 'Stationary stochastic processes for scientists and engineers' by G. Lindgren, H. Rootze'n, M. Sandsten, CRC Press, 2013, ISBN-13: 978-1-4665-8618-5,  is found at KFS studentbokhandel and other book stores. The book cover the whole course and includes the exercises for the tutorials.

Table of formulas 

Solution manual

Xtra exercises

Errata for the book

Exam

The course is concluded with a written exam, Friday November 2, 14.00-19.00, at Victoriastadion, Vic:2 and 3A.

The exam will be in english. You are allowed to bring a pocket calculator and the table of formulas of this course. You can also bring some small 'high school' table of formulas in mathematics (e.g. TEFYMA). Table of formulas must not contain any marks or comments.

 

 

Contact

Course responsible - Lecturer

Maria Sandsten 

046-222 49 53

Course secretary

Maria Lövgren

046-222 45 77

Question hours

Rachele Anderson, Ola Björnsson

Computer exercises

Rachele Anderson (coordinator), Ola Björnsson, Hampus Gustavsson, Maria Juhlin, Amanda Nilsson, Isabella Reinhold, Per Niklas Waaler