# New approximation for GARCH parameters estimate

## TL;DR

This paper introduces a novel optimization method for GARCH parameter estimation that uses local likelihood approximation and polynomial projections to improve maximum localization.

## Contribution

It proposes a new approach combining maximum localization and polynomial approximation for GARCH parameter estimation.

## Key findings

- Enhanced accuracy in GARCH parameter estimation
- Effective local likelihood approximation method
- Potential for improved financial time series modeling

## Abstract

This paper presents a new approach for the optimization of GARCH parameters estimation. Firstly, we propose a method for the localization of the maximum. Thereafter, using the methods of least squares, we make a local approximation for the projection of the likelihood function curve on two dimensional planes by a polynomial of order two which will be used to calculate an estimation of the maximum.