Time Series and Stochastic Processes ada 21 22

General course info

• Boring official web page

• tg-channel

• teams group: all class videos are there :)

• All home Assignments

• Notes for lectures and classes.

Teachers and assistants

Lecturer: Peter Lukianchenko

Class teacher: Boris Demeshev

Semester I

 [развернуть] 

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

Sources

• Wiki 2020-2021

• Git repo 2020-2021
• Git repo 2021-2022

• Statistics cookbook

MC + MCMC

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

• Cambridge course on Markov chains

• Chib and Greenberg, Understanding MH algorithm

• Casella, Explaining Gibbs Sampler

• Roberts and Rosenthal, General State Space Markov Chains

• Visualization of MCMC methods

• Charles Geyer, MCMC lecture notes (with a little bit of kernels!)

Stochastic Calculus

• Zastawniak, Basic Stochastic Processes

• Exams of ICEF master course

• Заметки магистерского курса МИЭФ (рус)

• Черновик учебника (рус)

• Черновик задачника (рус)

Time Series

• Forecasting principles and practice (R)

• Shumway, Stoffer Time Series Analysis

• Ruey Tsay web page

• Van der Vaart, Time Series

• Черновик задачника (рус)

UCM

• Harvey Jaeger, Detrending, Stylized Facts and the Business Cycle

• João Tovar Jalles, Structural Time Series Models and the Kalman Filter

• Harvey, Forecasting with UCM

• Chad Fulton

• Rob Hyndman, State Space Models