Recent reports suggest that the stochastic process underlying financial time series is nonstationary with nonstationary increments. Therefore, time averaging techniques through sliding intervals are inappropriate and ensemble methods have been proposed. Using daily ensemble averages we analyze...

The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called 'integration I(d)'. A class of regression models where cointegration works was identified by Granger and yields the ergodic behavior...

The discovery of the dynamics of a time series requires construction of the transition density. We explain why 1-point densities and scaling exponents cannot determine the class of stochastic dynamics. Time series require some sort of underlying statistical regularity to provide a basis for...

ARCH and GARCH models assume either i.i.d. or 'white noise' as is usual in regression analysis, while also 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...

Real financial markets are uncertain on the shortest trading time scales, therefore trading translates into noise. We discuss the pair correlations of detrended returns necessary to understand financial markets. Efficient markets and equilibrium markets generate conflicting pair correlations. B....