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.
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.
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:
