ARCH and GARCH Models vs. Martingale Volatility of Finance Market Returns

TL;DR

This paper critically examines ARCH and GARCH models, demonstrating their inconsistency with uncorrelated increments in financial returns and challenging their assumptions under the efficient market hypothesis.

Contribution

It reveals fundamental limitations of ARCH/GARCH models in representing financial market volatility, proposing that they violate key assumptions of uncorrelated increments and white noise.

Findings

ARCH/GARCH models are inconsistent with uncorrelated increments.

They violate the assumptions of white noise and i.i.d. in financial data.

The models conflict with the efficient market hypothesis.

Abstract

ARCH and GARCH models assume either i.i.d. or (what economists lable as) white noise as is usual in regression analysis while assuming memory in a conditional mean square fluctuation with stationary increments. We will show that ARCH/GARCH is inconsistent with uncorrelated increments, violating the i.i.d. and white assumptions and finance data and the efficient market hypothesis as well.