# Time Series and Stochastic Processes ada 21 22

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# 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

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

#### Week 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

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

Estimation of ETS and ARMA: colab notebook

## Sources

### MC + MCMC

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

### Stochastic Calculus

• Zastawniak, Basic Stochastic Processes