Time Series and Stochastic Processes ada 21 22 — различия между версиями

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(Week progress)
(Semester II)
 
(не показаны 23 промежуточные версии этого же участника)
Строка 9: Строка 9:
 
* [https://github.com/bdemeshev/tssp_2021-22/raw/main/ha/tssp_ha.pdf All home Assignments]
 
* [https://github.com/bdemeshev/tssp_2021-22/raw/main/ha/tssp_ha.pdf All home Assignments]
  
 +
* Notes for [https://github.com/bdemeshev/tssp_2021-22/tree/main/lectures lectures] and [https://github.com/bdemeshev/tssp_2021-22/tree/main/notes classes].
  
 
= Teachers and assistants =
 
= Teachers and assistants =
Строка 18: Строка 19:
  
  
= Week progress =
+
= Semester I =
 +
 
 +
<div class="mw-collapsible mw-collapsed" style="width:1000px; overflow: hidden;">
  
 
==== Week 01 ====
 
==== Week 01 ====
  
Lecture:
+
Lecture: [https://github.com/bdemeshev/tssp_2021-22/raw/main/lectures/Lect_01_TSSP.pdf]
  
 
Class: First step analysis, expected time to get HTH.
 
Class: First step analysis, expected time to get HTH.
Строка 28: Строка 31:
 
==== Week 02 ====
 
==== Week 02 ====
  
Lecture:
+
Lecture: [https://github.com/bdemeshev/tssp_2021-22/raw/main/lectures/Lect_02_TSSP.pdf]
  
 
Class: Markov chain states classification
 
Class: Markov chain states classification
Строка 35: Строка 38:
 
==== Week 03 ====
 
==== Week 03 ====
  
Lecture:  
+
Lecture: [https://github.com/bdemeshev/tssp_2021-22/raw/main/lectures/Lect_03_TSSP.pdf]
  
 
Class: Poisson process.  
 
Class: Poisson process.  
Строка 41: Строка 44:
 
==== Week 04 ====
 
==== Week 04 ====
  
Lecture:
+
Lecture: [https://github.com/bdemeshev/tssp_2021-22/raw/main/lectures/Lect_04_TSSP.pdf]
  
Class:  
+
Class: Conditional expected value. Conditional variance.
  
 
==== Week 05 ====
 
==== Week 05 ====
  
Lecture:
+
Lecture: [https://github.com/bdemeshev/tssp_2021-22/raw/main/lectures/Lect_05_TSSP.pdf]
  
Class: Conditional expected value. Conditional variance.
+
Class: Sigma-algebras, measurability. Conditional expected value with respect to sigma-algebra.
  
 
==== Week 06 ====
 
==== Week 06 ====
Строка 55: Строка 58:
 
Lecture:
 
Lecture:
  
Class: Sigma-algebras, measurability. Conditional expected value with respect to sigma-algebra.
+
Class: Probability limit, Moment generating function
  
==== Week 07 ====
+
 
 +
==== Midterm ====
 +
 
 +
The long-awaited midterm will be on 28 October, 10:00 - 12:00.
 +
 
 +
Duration: 120 minutes. No proctoring.
 +
 
 +
Topics:
 +
* First step analysis
 +
* Classification of states and classes of MC.
 +
* Conditional expected value (two views).
 +
* Poisson process.
 +
* Sigma algebras.
 +
* Probability limit
 +
* Moment generating function
 +
 
 +
 
 +
==== Week ====
 +
 
 +
Date: 2021-10-28
  
 
Lecture:
 
Lecture:
  
Class: Probability limit, Moment generating function
+
Class: Martingales in discrete time
 +
 
 +
 
 +
==== Week  ====
 +
 
 +
Date: 2021-11-09
 +
 
 +
Lecture:
 +
 
 +
Class: Wiener process definition, basic properties, inversion
 +
 
 +
==== Week  ====
 +
 
 +
Date: 2021-11-16
 +
 
 +
Lecture:
 +
 
 +
Class: Stochastic integral, intuition, limit in L2
 +
 
 +
==== Week  ====
 +
 
 +
Date: 2021-11-23
 +
 
 +
Lecture:
 +
 
 +
Class: Stochastic integral properties, Ito's lemma
 +
 
 +
==== Week  ====
 +
 
 +
Date: 2021-11-30
 +
 
 +
Lecture:
 +
 
 +
Class: BS model, Girsanov theorem, pricing
 +
 
 +
==== Week  ====
 +
 
 +
Date: 2021-12-07
 +
 
 +
Lecture:
 +
 
 +
Class: more pricing examples in BS model
 +
 
 +
==== Week  ====
 +
 
 +
Date: 2021-12-14
 +
 
 +
Lecture:
 +
 
 +
Class: Recap on martingales, Ito, etc
 +
 
 +
</div>
 +
 
 +
= Semester II =
 +
 
 +
Do not forget about [https://github.com/bdemeshev/tssp_2021-22/raw/main/ha/tssp_ha.pdf the home assignments!]
 +
 
 +
==== Week 1 ====
 +
 
 +
[https://github.com/bdemeshev/tssp_2021-22/raw/main/lectures/TSSP_m3_l1_done.pdf Lecture 1]. White noise, stationarity, ACF, PACF
 +
 
 +
1.1.
 +
 
 +
1.2. Predictive interval for random walk, difference between mean, mode and median: [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-01-14-sem2_class_01_2_b.pdf pdf-b]
 +
 
 +
==== Week 2 ====
 +
 
 +
[https://github.com/bdemeshev/tssp_2021-22/raw/main/lectures/TSSP_m3_l2_done.pdf Lecture 2].
 +
 
 +
2.1. ETS model, forecasting, decomposition: [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-01-18-sem2_class_02_1_a.pdf pdf-a], [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-01-18-sem2_class_02_1_b.pdf pdf-b], [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-01-18-sem2_class_02_1_c.pdf pdf-c]
 +
 
 +
2.2. AR(2), expected value, covariances: [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-01-20-sem2_class_02_2_a.pdf pdf-a], [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-01-20-sem2_class_02_2_b.pdf pdf-b], [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-01-20-sem2_class_02_2_c.pdf pdf-c]
 +
 
 +
[https://github.com/bdemeshev/tssp_2021-22/raw/main/arma_no_nonsense/arma_no_nonsense.pdf Arma notes without nonsense]
 +
 
 +
==== Week 3 ====
 +
 
 +
[https://github.com/bdemeshev/tssp_2021-22/raw/main/lectures/TSSP_m3_l3_done.pdf Lecture 3].
 +
 
 +
3.1. Non stationarity of ETS(AAA), solutions of recurrence equation: [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-01-26-sem2_class_03_1_b.pdf, pdf-b]
 +
 
 +
3.2. Equations is not a process.
 +
Two problems from [https://new.universiade-ecm.com/ Econometrics Olympiad]: [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-01-27-sem2_class_03_2_a_rus.pdf pdf-a], [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-01-27-sem2_class_03_2_b_eng.pdf pdf-b], [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-01-28-sem2_class_03_2_c_rus.pdf pdf-c].
 +
 
 +
==== Week 4 ====
 +
 
 +
[https://github.com/bdemeshev/tssp_2021-22/raw/main/lectures/TSSP_m3_l4_done.pdf Lecture 4].
 +
 
 +
4.1. Solutions of recurrence equation: [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-02-01-sem2_class_04_1_a_rus_arma_sols.pdf pdf-a], [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-02-01-sem2_class_04_1_b_rus_arma_sols.pdf pdf-b], [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-02-01-sem2_class_04_1_c_eng_arma_sols.pdf pdf-c].
 +
 
 +
4.2. Roots of lag and characteristic equation: [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-02-03-sem2_class_04_2_a_eng_roots.pdf pdf-a], [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-02-03-sem2_class_04_2_b_rus_roots.pdf pdf-b], [https://github.com/bdemeshev/tssp_2021-22/raw/main/notes/tssp_2021-22_2022-02-03-sem2_class_04_2_c_rus_roots.pdf pdf-c].
 +
 
 +
==== Week 5 ====
 +
 
 +
[https://github.com/bdemeshev/tssp_2021-22/raw/main/lectures/TSSP_m3_l5_done.pdf Lecture 5]
 +
 
 +
Estimation of ETS and ARMA: [https://colab.research.google.com/drive/1LE9T0KnnUBM-1OIzWT3INJzJjKd5-GdX?usp=sharing colab notebook]
 +
 
 +
==== Week 6 ====
 +
 
  
  
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== Sources ==
 
== Sources ==
 +
 +
* [http://wiki.cs.hse.ru/Time_Series_and_Stochastic_Processes_ada_20_21 Wiki 2020-2021]
 +
 +
* [https://github.com/bdemeshev/tssp/tree/master/2020_2021 Git repo 2020-2021]
 +
* [https://github.com/bdemeshev/tssp_2021-22/ Git repo 2021-2022]
  
 
* [https://github.com/mavam/stat-cookbook/releases/download/0.2.6/stat-cookbook.pdf Statistics cookbook]
 
* [https://github.com/mavam/stat-cookbook/releases/download/0.2.6/stat-cookbook.pdf Statistics cookbook]
Строка 77: Строка 203:
 
* [http://www.statslab.cam.ac.uk/~rrw1/markov/ Cambridge course] on Markov chains
 
* [http://www.statslab.cam.ac.uk/~rrw1/markov/ Cambridge course] on Markov chains
  
* [https://eml.berkeley.edu/reprints/misc/understanding.pdf Chib and Greenberg, Understanding MH algorithm]
+
* Chib and Greenberg, [https://eml.berkeley.edu/reprints/misc/understanding.pdf Understanding MH algorithm]
  
* [http://biostat.jhsph.edu/~mmccall/articles/casella_1992.pdf Casella, Explaining Gibbs Sampler]
+
* Casella, [http://biostat.jhsph.edu/~mmccall/articles/casella_1992.pdf Explaining Gibbs Sampler]
  
* [http://www.statslab.cam.ac.uk/~rrw1/markov/index.html  (no kernels)]
+
* Roberts and Rosenthal, [https://projecteuclid.org/euclid.ps/1099928648 General State Space Markov Chains]
 
+
* [https://projecteuclid.org/euclid.ps/1099928648 General State Space Markov Chains by Roberts and Rosenthal (+++, статья)]
+
  
 
* [https://chi-feng.github.io/mcmc-demo Visualization of MCMC methods]
 
* [https://chi-feng.github.io/mcmc-demo Visualization of MCMC methods]
  
* [http://www.stat.umn.edu/geyer/f05/8931/n1998.pdf Charles Geyer, MCMC lecture notes (with a little bit of kernels!)]
+
* Charles Geyer, [http://www.stat.umn.edu/geyer/f05/8931/n1998.pdf MCMC lecture notes] (with a little bit of kernels!)
 
+
 
+
  
 
=== Stochastic Calculus ===
 
=== Stochastic Calculus ===
Строка 111: Строка 233:
 
* [https://faculty.chicagobooth.edu/ruey-s-tsay/teaching Ruey Tsay web page]
 
* [https://faculty.chicagobooth.edu/ruey-s-tsay/teaching Ruey Tsay web page]
  
* [http://www.math.leidenuniv.nl/~avdvaart/timeseries/index.html van der Vaart]
+
* Van der Vaart, [http://www.math.leidenuniv.nl/~avdvaart/timeseries/index.html Time Series]
  
 
* [https://github.com/bdemeshev/ts_pset Черновик задачника (рус)]
 
* [https://github.com/bdemeshev/ts_pset Черновик задачника (рус)]
Строка 117: Строка 239:
 
==== UCM ====
 
==== UCM ====
  
* [https://www.statsmodels.org/dev/examples/notebooks/generated/statespace_structural_harvey_jaeger.html aa]
+
* Harvey Jaeger, [https://www.statsmodels.org/dev/examples/notebooks/generated/statespace_structural_harvey_jaeger.html Detrending, Stylized Facts and the Business Cycle]
  
* [https://core.ac.uk/download/pdf/6242335.pdf bb]
+
* João Tovar Jalles, [https://core.ac.uk/download/pdf/6242335.pdf Structural Time Series Models and the Kalman Filter]
  
 
* [https://pdfs.semanticscholar.org/0bc8/582016086017763b93e87ad8640ec1816aeb.pdf Harvey, Forecasting with UCM]
 
* [https://pdfs.semanticscholar.org/0bc8/582016086017763b93e87ad8640ec1816aeb.pdf Harvey, Forecasting with UCM]
Строка 126: Строка 248:
  
 
* [https://robjhyndman.com/uwafiles/9-StateSpaceModels.pdf Rob Hyndman, State Space Models]
 
* [https://robjhyndman.com/uwafiles/9-StateSpaceModels.pdf Rob Hyndman, State Space Models]
 
  
 
== Grading System ==
 
== Grading System ==

Текущая версия на 18:08, 12 февраля 2022

General course info

Teachers and assistants

Lecturer: Peter Lukianchenko

Class teacher: Boris Demeshev


Semester I

Week 01

Lecture: [1]

Class: First step analysis, expected time to get HTH.

Week 02

Lecture: [2]

Class: Markov chain states classification


Week 03

Lecture: [3]

Class: Poisson process.

Week 04

Lecture: [4]

Class: Conditional expected value. Conditional variance.

Week 05

Lecture: [5]

Class: Sigma-algebras, measurability. Conditional expected value with respect to sigma-algebra.

Week 06

Lecture:

Class: Probability limit, Moment generating function


Midterm

The long-awaited midterm will be on 28 October, 10:00 - 12:00.

Duration: 120 minutes. No proctoring.

Topics:

  • First step analysis
  • Classification of states and classes of MC.
  • Conditional expected value (two views).
  • Poisson process.
  • Sigma algebras.
  • Probability limit
  • Moment generating function


Week

Date: 2021-10-28

Lecture:

Class: Martingales in discrete time


Week

Date: 2021-11-09

Lecture:

Class: Wiener process definition, basic properties, inversion

Week

Date: 2021-11-16

Lecture:

Class: Stochastic integral, intuition, limit in L2

Week

Date: 2021-11-23

Lecture:

Class: Stochastic integral properties, Ito's lemma

Week

Date: 2021-11-30

Lecture:

Class: BS model, Girsanov theorem, pricing

Week

Date: 2021-12-07

Lecture:

Class: more pricing examples in BS model

Week

Date: 2021-12-14

Lecture:

Class: Recap on martingales, Ito, etc

Semester II

Do not forget about the home assignments!

Week 1

Lecture 1. White noise, stationarity, ACF, PACF

1.1.

1.2. Predictive interval for random walk, difference between mean, mode and median: pdf-b

Week 2

Lecture 2.

2.1. ETS model, forecasting, decomposition: pdf-a, pdf-b, pdf-c

2.2. AR(2), expected value, covariances: pdf-a, pdf-b, pdf-c

Arma notes without nonsense

Week 3

Lecture 3.

3.1. Non stationarity of ETS(AAA), solutions of recurrence equation: pdf-b

3.2. Equations is not a process. Two problems from Econometrics Olympiad: pdf-a, pdf-b, pdf-c.

Week 4

Lecture 4.

4.1. Solutions of recurrence equation: pdf-a, pdf-b, pdf-c.

4.2. Roots of lag and characteristic equation: pdf-a, pdf-b, pdf-c.

Week 5

Lecture 5

Estimation of ETS and ARMA: colab notebook

Week 6

Sources

MC + MCMC

  • James Norris, Markov chains (1998, no kernels)

Stochastic Calculus

  • Zastawniak, Basic Stochastic Processes

Time Series

UCM

Grading System