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

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.