Time Series and Stochastic Processes ada 20 21

General course info

• Boring official web page

• tg-channel

• All home Assignments

• [Grades](https://docs.google.com/spreadsheets/d/1PQmrMM9usDrDs2oAjJJpGCUmFw6B53pDg5T4VBZmm4s/edit?usp=sharing)

This course is conducted at Data Science and Business Analytics program and is provided to 3rd-year undergraduates who have studied a course covering basic probability and statistical inference. A half of this course introduces concepts of Markov chains, random walks, martingales as well as of to the time series. The course requires basic knowledge in probability theory and linear algebra. It introduces students to the modeling, quantification and analysis of uncertainty. The main objective of this course is to develop the skills needed to do empirical research in fields operating with time series data sets. The course aims to provide students with techniques and receipts for estimation and assessment of quality of economic models with time series data. The course will also emphasize recent developments in Time Series Analysis and will present some open questions and areas of ongoing research.

Week progress

Week 01

• Sigma-algebras, measurability of random variable with respect to sigma-algebra.
• Seminar 01

Week 02

• Markov chain. Classification of states. Calculations of return probability, mean return time, stationary distribution.
• Seminar 02a, 02b
• Cambridge Markov chain course. There you may find useful: lecture notes, past tripos and more.

Week 03

• Conditional expected value. Martingales.

Week 04

• Abracadabra martingale

Week 05

• Wiener process: basic properties, inversion

Week 06

• Wiener process: limit in L2

Week 07

Ito integral WtdWt, Ito's lemma

Sources

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

• Черновик задачника (рус)

UCM

• aa

• bb

• Harvey, Forecasting with UCM

• Chad Fulton

• Rob Hyndman, State Space Models

MC + MCMC

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

• Cambridge course on Markov chains

• Chib and Greenberg, Understanding MH algorithm

• Casella, Explaining Gibbs Sampler

• (no kernels)

• General State Space Markov Chains by Roberts and Rosenthal (+++, статья)

• Visualization of MCMC methods

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

Grading System

Interim assessment (2 module):
0.400 FallMock
0.400 Winter Mock
0.200 Homework

Interim assessment (4 module):
0.650 UoL Exam
0.100 Final Exam
0.100 Homework
0.100 Spring Mock
0.050 Quizzes