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Travel Plan I have always been dreaming of traveling to Hawaii and enjoy the beach and sunshine. This spring break we got cheap tickets and make our plan to...

EM Algorithm for Linear Clusters

Here is an interesting situation occurred to me. In a scatter plot, it is clear that there are two straight lines and each line is contanminated by some nois...

Some FPGA basic element design and Vivado code

I am doing a service task for CERN on a hardware project. I learned something on FPGA and some basic vivado code and glad to share here.

Introduction on how to write an Athena(ATLAS) package for release22

I am writing this post is because I recently met some problem of writing an Athena Algorithm for my research. I am using a simple code to get lepton n-tuples...

Some Properties of Linear Regression

If we regress $X$ on $Y$ and get $\beta$ as the slope and if we regress $Y$ on $X$ and get slope $\beta’$. What is the product of $\beta$ and $\beta’$

Interesting Statsitcal Problems in Interviews

Problem 1 If we have $n$ dice draws with a dice that has $k$ sides. Let $X_i$ to be the random variables that describes the number of times that the dice fac...

Lecture 01 (Jan 21, 2022)

First Lecture: Intorduction of autocorrleation for linear time series

Lecture 02 (Jan 24, 2022)

Calculate the variance and convergence rates for autocorrelation sample estimator by central limit theorem. Introduce statistical tests for ACF.

Lecture 03 (Jan 26, 2022)

Some introduction of AR model and linear model covariance calculation.

Lecture 04 (Jan 31, 2022)

Introduce AR(2) model and disucss the condition of weakly stationary for AR(1) and AR(2) models

Lecture 05 (Feb 02, 2022)

Periodicity of AR models with complex roots; Asymptotic statistics of AR(p) models

Lecture 06 (Feb 04, 2022)

Introduction to PACF and Information criteria (AIC, BIC)

Lecture 07 (Feb 07, 2022)

Introduction to MA model and conditional loglikelihood maximization method. Introdcution to ARMA model

Lecture 08 (Feb 09, 2022)

Introduction to ARMA model and its AR and MA representation

Lecture 09 (Feb 11, 2022)

Introduction of Karhunen-Leove theorem, the spectral theorem and autocovariance generating function

Lecture 10 (Feb 14, 2022)

Spectral density as the Fourier transform of autocovariance, the sample version spectral representation theory and sample periodogram

Lecture 11 (Feb 16, 2022)

Spectral representation sample version proof. Variance decomposition into Fourier components. Estimate spectral density

Lecture 12 (Feb 18, 2022)

Non parametric estimation of spectral density (Kernel Method)

Lecture 13 (Feb 21, 2022)

Introduction to Conditional Variance

Lecture 14 (Feb 23, 2022)

Introduction to ARCH model

Lecture 15 (Feb 25, 2022)

Estimation of ARCH Model with method of moments

Lecture 16 (Feb 28, 2022)

Introduction to Generalized ARCH and model estimation and forecast

Lecture 17 (March 02, 2022)

Introduction to Non-linear Models including TAR ans SETAR

Lecture 18 (March 04, 2022)

Introduction to unit root models

Lecture 19 (March 07, 2022)

Construct statistical test for unit root from samples

Lecture 20 (March 09, 2022)

Random Walk with Drift term and statistical test for non-zero drift

Lecture 21 (March 11, 2022)

Statistical Test for The Drift Term

Lecture 22 (March 21, 2022)

Continuous Time Model

Lecture 23 (March 23, 2022)

Introduction to Ito’s Process and Ito’s Lemma

Lecture 24 (March 25, 2022)

Introduction to Ito’s Process and Ito’s Lemma

Lecture 25 (March 28, 2022)

Application of Ito’s Lemma: Derivation of Black-Scholes Formula

Lecture 26 (March 30, 2022)

Diffusion Processes with Jumps

Lecture 27 (April 01, 2022)

Continutation of Jump Diffusion Model and Introduction to Multiple Time Series

Lecture 28 (April 04, 2022)

Introduction to Vector Autoregressive (VAR) model

Lecture 29 (April 06, 2022)

Introduction to Cointegration and Vector Error Correction Model

Lecture 30 (April 08, 2022)

Introduction to Vector Error Correction Model

Lecture 31 (April 11, 2022)

Introduction to state space model, the Kalman Filterl

Lecture 32 (April 13, 2022)

Continuation of the discussion of Kalman Filter

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