imported>Bdemeshev: /* Sources of Wisdom */

2025-01-16T16:35:22Z

Sources of Wisdom

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== What-about ==

Course [https://github.com/bdemeshev/hse_panda_metrics_2024_2025/raw/main/whitepaper.pdf whitepaper]

=== Course goals ===

侍には目標がなく道しかない [Samurai niwa mokuhyō ga naku michi shikanai]

A samurai has no goal, only a path.

Telegram [https://t.me/+qQ48C4bmlNUzNTc6 chat]

== Grading ==

Stochastic Processes = 0.35 Halloween Exam + 0.40 Ded Moroz Exam + 0.25 Home Assignments

Time Series Analysis = 0.30 Mimoza Exam + 0.45 Sakura Exam + 0.25 Home Assignments

=== Home assignments ===

[https://github.com/bdemeshev/hse_panda_tssp_2024_2025/raw/main/home_assignments/home_assignments.pdf Home assignments :)]

Home assignments have equal weights. You have 4 honey weeks for the whole year.

=== Exams ===

[https://github.com/bdemeshev/tssp_exams/raw/main/tssp_exams.pdf Past exams]

'''Midterm alpha: Tuesday, 5 November at 18:10.'''

== Samurai diary: Stochastic Process ==

<div class="mw-collapsible mw-collapsed" style="width:1000px; overflow: hidden;">

Lecture slides and class [https://github.com/bdemeshev/hse_panda_tssp_2024_2025/tree/main/course_notes notes]

2024-09-02, lecture 1:

2024-09-09, lecture 2:

2024-09-16, lecture 3: Markov chain: communicating classes. Transient states. Recurrent states.

2024-09-24, lecture 4: Idea of generating function: describe collection of objects as a function and extract information from function.
How to extract E(X), E(X^2), E(XY), P(X=3) from a function that generates outcomes. Formal definition of probability generating function and moment generating function.

2024-10-30, lecture 5:

2024-10-07, lecture 6:

2024-10-14, lecture 7: Sigma-algebra is a way to model information, formal definition. Calculating sigma-algebra generated by two events or by discrete random variable.
Filtration is a growing sequence of sigma-algebras. Formal definition of conditional expected value with respect to sigma-algebra.

2024-10-21, lecture 8:

2024-12-02, lecture: Girsanov theorem, European option pricing in the Black and Scholes model

=== Classes ===

Class [https://e.pcloud.link/publink/show?code=kZDCKPZ6dPB3lXGHrhUzqeC7wkVfyaLsAq7 video recordings]

Maria Kirillova [https://disk.yandex.ru/d/5gs97BDSjwmOSw notes]

2024-09-06, class 1: First step analysis, 1.1 from [https://github.com/bdemeshev/stochastic_pro/raw/main/stochastic_pro.pdf StoPro].

More on first step analysis: section 2.7.2 in [https://projects.iq.harvard.edu/stat110/home In2Pro]

2024-09-13, class 2: First step analysis, 1.4 from [https://github.com/bdemeshev/stochastic_pro/raw/main/stochastic_pro.pdf StoPro].

2024-09-20, class 3: Classification of states in Markov chain, communicating classes, 3.1ab from [https://github.com/bdemeshev/stochastic_pro/raw/main/stochastic_pro.pdf StoPro].

2024-09-27, class 4: Generating functions: standard normal distribution, chi-squared with 1 degree of freedom.

2024-10-04, class 5: Calculating probability limit using LLN. Intuition behind probability limit: unique forecast that is "arbitrary good" for almost all X_n.
Probability limit of max and min. Probability limit is a random variable. Probability limit of iid sequence does not exist.

2024-10-11, class 6: Two more limits (in probability and in L2), conditional expected value in uniform case, conditional expected value with joint density.

2024-10-18, class 7: Calculation of sigma-algebra generated by random variable. Calculation of expected value wrt to sigma-algebra.

2024-11-01, class 8: Checking that a process is a martingale, 9.1abcd, 9.9 from [https://github.com/bdemeshev/stochastic_pro/raw/main/stochastic_pro.pdf StoPro].

2024-11-08, class 9: Poisson point process

2024-11-15, class 10: Doob's optional stopping time theorem in discrete time

2024-11-22, class 11: Calculating E, Cov, Var for Wiener process, (W_t) and (W_t^2 - t) are martingales

2024-11-29, class 12: Ito's integral for a piece-wise constant process, Ito's lemma, martingale condition

2024-12-06, class 13: more Ito's lemma and stochastic integral properties.

2024-12-13, class 14: binomial tree, finding risk neutral probabilities, European and American call option.

</div>

== Samurai diary: Time series ==

2025-01-09, lecture 1: Weakly and strictly stationary processes: definition, examples, MA(q) process, autocovariance and autocorrelation function

2025-01-16, lecture 2: Non-uniqueness of MA(q) equation, invertibility of MA(q) process: definition and criterion, characteristic MA-polynomial, MA(infty) process, AR(p)-equation, example of infinitely many solutions of AR(1)-equation.

2025-01-17, class 1: Stationarity, MA-process

== Sources of Wisdom ==

[https://github.com/bdemeshev/stochastic_pro/raw/main/stochastic_pro.pdf StoPro]: Problems in Stochastic Processes

[https://projects.iq.harvard.edu/stat110/home In2Pro]: Blitstein, Hwang, Introduction to probability.

[https://aditya-sengupta.github.io/expository/markovtex.pdf MarkovTex]: Representing Markov Chains in Latex.

[https://www.statslab.cam.ac.uk/~rrw1/markov/M.pdf Mchains] Cambridge lectures on Markov chains.

[https://www.stat.berkeley.edu/~aldous/150/takis_exercises.pdf Takis]: Takis Konstantinopulos, One hundred solved exercises on Markov chains.

[https://courses.cit.cornell.edu/econ620/reviewm6.pdf Convergence modes] review from Cornell university

[https://www.ee.iitb.ac.in/~sarva/courses/EE325/2014/Slides/ConvergenceOfRVs.pdf Convergence modes]: Saravan Vijayakumaran, convergence modes with examples

[https://staff.fnwi.uva.nl/p.j.c.spreij/onderwijs/master/aadtimeseries2010.pdf ts2010]: Aad van der Vaart, Time Series course with hardcore math

Past course iterations: [http://wiki.cs.hse.ru/Tssp-2023-24 2023-2024], [http://wiki.cs.hse.ru/Tssp-2022-23 2022-2023], [http://wiki.cs.hse.ru/Time_Series_and_Stochastic_Processes_ada_21_22 2021-2022], [http://wiki.cs.hse.ru/Time_Series_and_Stochastic_Processes_ada_20_21 2020-2021].

Tssp-2024-25 - История изменений

imported>Bdemeshev: /* Sources of Wisdom */