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Stationary Stochastic Processes

News HT 2017

The registration system opens for Comp. exercise 2: September 19. 

Important: If you become ill and can not attend the occasion you have registered for, you should notify the course secretary before the exercise starts, by E-mail or by phone.

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 Monday September 25 at 12.00 noon. 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 2 by tpi07xyz" (one student) or  "Assignment 2 by tfy08xyz and nat09xyz" (two students). 

The extra files for the exercises are found here.

 

Note: An error has shown upon the preparation for the computer exercise 1: Exercise 3) in the question dictionary should be to find the confidence interval of m, not for V[mhat]. The tutorial below is now updated to be correct.

The computer exercises are mandatory and the registration system opens for Comp. exercise 1: September 5. 

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 Monday September 11 at 12.00 noon. 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.

Welcome to Stationary Stochastic Processes!

The first lecture is Monday August 28 13.15-15.00 in MH:Rieszsalen.

Preliminary schedule for the course is given below.

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:Rieszsalen.  

 

Lectures with preliminary schedule

  1. Mon August 28 13.15-15.00 Chapter 1 and 2: Lecture 1, Ch. 1.1, 1.2, 2.2.1, 2.2.2, 2.3.2, 2.5.2
  2. Tue August 29 10.15-12.00 Chapter 2: Lecture 2, Ch. 2.2.3, 2.3.1, 2.3.3, 2.4.1, 2.4.2, 2.5.1, (2.5.2), (2.5.3), (2.6)
  3. Mon Sept 4  13.15-15.00 Chapter 4: Lecture 3, Ch. 4.1, 4.2.1, 4.2.2, 4.2.3, 4.2.4, 4.3.1, (4.3.2)  
  4. Tue Sept 5 10.15-12.00 Chapter 4: Lecture 4, Ch. 4.4, 4.5.1
  5. Mon Sept 11 13.15-15.00 Chapters 5 and 6: Lecture 5, Ch. 5.1, 5.2, 6.1, 6.2  
  6. Tue Sept 12 10.15-12.00 Chapters 6 and 7: Lecture 6, Ch. 6.5, 7.1, 7.2.1
  7. Mon Sept 18 13.15-15.00 Chapter 7: Lecture 7, Ch. 7.2.1, 7.2.2, 7.2.3, (7.3), (7.4.1)
  8. Tue Sept 19 10.15-12.00 Chapters 8, 6 and 5: Lecture 8, Ch. (8.1), (8.2), (6.3.1), 6.3.2, (6.4), 5.3.1   
  9. Mon Sept 25 13.15-15.00 Chapter 8: Lecture 9, Ch. 8.4, 8.5 
  10. Mon Oct 2 13.15-15.00 Chapter 9: Lecture 10, Ch. 9.1, 9.2, 9.3, 9.4, 9.5
  11. Tue Oct 3 10.15-12.00 Summary and old exams

 

Weekly Exercise schedule (preliminary)

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. The exercises numbered with letters are found in the additional material. 

  1. Week 1: (August 28 - September 1) 2.1(-1), 2.2(-1), 2.3(0), 2.4(+1), 2.6(0), 2.8(+1), 2.9(0), 2.10(+1), 2.11(0), 2.12(+1), 2.13(0), 2.14(0), 2.15(+1), 2.16(0), 2.18(0). Example1.pdf, Example1-with-sound.mp4, Example2.pdf, Example2-with-sound.mp4
  2. Week 2: (September 4 - September 8) 4.1(-1), 4.2(-1), 4.3(0), 4.4(-1), 4.5(0), 4.6(0), 4.7(0), COMB1(+1), 4.9(0), COMB2(0), COMB3(-1), 4.10(0), SAMP1(0), SAMP2(0), SAMP3(+1), SAMP4(+1), 4.11(+1): Additional-exercises-week2.  Example3.pdfExample3-with-sound.mp4Example4.pdfExample4-with-sound.mp4
  3. Week 3: (September 11 - September 15) 5.1(-1), 5.2(0), 5.3(0), 5.4(+1), 5.5a(+1), 6.1(0), 6.2(0), 6.3(-1), FILT1(-1), FILT2(0), FILT3(0), 6.4(+1), 6.5(0), FILT4(+1), 6.9(0), 6.10(+1), FILT5(+1), FILT6(+1): Additional exercises week3 . Example5.pdf, Example6.pdf
  4. Week 4: (September 18 - September 22) 7.1(0), 7.2(0), 7.3(0), ARMA1(-1), 7.4(0), 7.5(+1), 7.6(+1), ARMA2(-1), 7.7(0), ARMA3(0), ARMA4(0), ARMA5(0), 7.8(-1), ARMA6(+1), 7.9(+1), 7.10(+1), 7.12(0), 7.13(+1), 7.15(+1): Additional exercises week4. Example7.pdf, Example8.pdf
  5. Week 5: (September 25 - September 29) 6.7(0), 6.8(0), DIFF1(0), DIFF2(0), DIFF3(+1), DIFF4(+1), DIFF5(+1), 5.6(+1), 8.2(0), 8.3(0), 8.4(+1), 8.5(0), 8.7(0), 8.9(+1): Additional exercises week5 
  6. Week 6: (October 2 - October 6) 9.1(0), 9.2(+1), 9.3(0), 9.4(0), 9.5(0), SPEKT1(0), SPEKT2(0), SPEKT3(+1), SPEKT4(+1), SPEKT5(0), SPEKT6(0): Additional exercises week6       
  7. Week 7: Review and old exams, see below.

 

Question Times 

  • Thu Aug 31 8.15-10.00, MH:362A: Thu Aug 31 13.15-15.00, MH:331: Fri Sept 1 13.15-15.00, MH:331.
  • Thu Sept 7 8.15-10.00, MH:362A: Thu Sept 7 13.15-15.00, MH:331: Fri Sept 8 13.15-15.00, MH:331.
  • Thu Sept 14 8.15-10.00, MH:362A: Thu Sept 14 13.15-15.00, MH:331: Thu Sept 14 15.15-17.00, MH:331.
  • Thu Sept 21 8.15-10.00, MH:362A: Thu Sept 21 13.15-15.00, MH:331: Fri Sept 22 13.15-15.00, MH:331.
  • Thu Sept 28 8.15-10.00, MH:362A: Thu Sept 28 13.15-15.00, MH:331: Fri Sept 29 13.15-15.00, MH:331.
  • Thu Oct 5 8.15-10.00, MH:362A: Thu Oct 5 13.15-15.00, MH:331: Fri Oct 6 13.15-15.00, MH:331.
  • Thu Oct 12 8.15-10.00, MH:362A: Thu Oct 12 13.15-15.00, MH:331: Fri Oct 13 13.15-15.00, MH:331.

 

Additional Question Times for the Exam

Mon Oct 16 10.15-12.00 MH:331, 

Thu Oct 19 10.15-12.00 MH:227, 

Tue Oct 24 10.15-12.00 MH:227, 

Thu Oct 26 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 12 13.15-15.00 (E:Hacke, E:Panter)
  • Wed Sept 13 10.15-12.00 (E:Satu, E:Uran)  
  • Wed Sept 13 13.15-15.00 (E:Hacke)
  • Fri Sept 15 10.15-12.00 (E:Elg, E:Elgkalv)

Comp. exercise 2:

  • Tue Sept 26 10.15-12.00 (E:Nept, E:Uran)
  • Tue Sept 26 13.15-15.00 (E:Hacke, E:Panter)
  • Wed Sept 27 13.15-15.00 (E:Hacke)
  • Fri Sept 29 10.15-12.00 (E:Satu, E:Uran)

Comp. exercise 3:

  • Tue Oct 10 13.15-15.00 (E:Hacke, E:Panter)
  • Wed Oct 11 10.15-12.00 (E:Elg, E:Elgkalv)
  • Wed Oct 11 13.15-15.00 (E:Satu, E:Uran)
  • Fri Oct 13 10.15-12.00 (E:Elg)

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

Errata for the book

Exam

The course is concluded with a written exam, Saturday October 28, 8.00-13.00, at Victoriastadium, 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.

 

 

Advanced courses

The slides from the short presentation of advanced courses are found here.

 

 

 

 

Contact

Course responsible - Lecturer

Maria Sandsten 

046-222 49 53

Course secretary

Maria Lövgren

046-222 45 77

Question hours

Rachele Anderson, Zite He (Ted), Isabella Reinhold

 

Computer exercises

Isabella Reinhold, Rachele Anderson (coordinators), Zite He, Francisco Mendoza, Andrew Segar, Imran Sheikh