Time Series and Stochastic Processes ada 21 22

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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