Time Series and Stochastic Processes ada 20 21

General course info

• Boring official web page

• tg-channel

• All home Assignments

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!)