Sunday, April 13, 2025

Fossilized Wonders Youmu ver. - Touhou 20 Fan-Art


PNG version


 Posted on my pixiv page: https://www.pixiv.net/en/artworks/129288230

News letter from ZUN about Touhou 20: https://touhou-project.news/news/13976/


 

 I have illustrated it to commemorate a release of the latest Touhou Project series, Touhou 20 ~Fossilized Wonders~ ! ... pity that Myonchan (Youmu Konpaku) is not in this title as a playable character which I have expected. At the same time, I reckon that the title design of this game rather suits for that, and then I decided to draw it with her. The ZUN style design refers to the latest of hers in Touhou 17 ~ Wily Beast and Weakest Creature~ This is the fusion of ZUN's style and my own.

 



Tuesday, April 08, 2025

Financial time series analysis with Matrix Pencil, the modern Prony's method - Python, Future prediction, Yahoo finance

 Originally Saturday, November 30, 2024

 The misprints of the elements in unitary-matrices in the recipe corrected on Tuesday 8th April 2025





The misprints  the elements in unitary-matrices in the recipe corrected on Tuesday 8th April 2025

 

 


 

Friday, March 28, 2025

Engle's ARCH motion prediction model with the simulation data with Python

 This is introduced in my cartoon video of Yukkuri Kaisetsu (Touhou Project fan-art):




Auto-Regressive Conditional Heteroscedasticity (ARCH)

ARCH was developed by an economist Robert F. Engle III having won the 2003 Nobel Memorial Prize in Economic Sciences for its achievement.

Dependent variable: the variance error terms of the first regression:
The explanatory variable X can be the lagged dependent variables and/or the other variables: 
Then, it find the coefficient γ of the lagged squared error terms with reference to the log-likelihood: 
 

Generalised Auto-Regressive Conditional Heteroscedasticity (GARCH)

GARCH assumes the variance of the error term symmetrically varies depending the average size of the error terms in pervious time steps. It adds the lagged variance on the explanatory variable of the second regression with reference to the log-likelihood for finding the coefficients γ and δ:

 

 Simulation Data with Python

The following exhibits display the simulation data evaluated using ARCH to illustrate how ARCH functions.

To facilitate the visual representation of this simulation, the most basic form of Engle's ARCH, as introduced in the Wikipedia entry below, has been implemented.

Ref: https://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity

This simplified simulation demonstrates motion prediction for intercepting incoming flying projectiles with erratic movements, resembling the fluctuations of a stock price.

Following is my Python codes: