105 citations · 529 across the 26 of their papers we have counts for
4 papers · 1 filter
Anomalous Scaling of Stochastic Processes and the Moses Effect
Lijian Chen, Kevin E. Bassler, Joseph L. McCauley +1
The state of a stochastic process evolving over a time is typically assumed to lie on a normal distribution whose width scales like . However, processes where the prob…
Time vs. Ensemble Averages for Nonstationary Time Series
Joseph L. McCauley
We analyze the question whether sliding window time averages applied to stationary increment processes converge to a limit in probability. The question centers on averages, correla…
ARCH and GARCH Models vs. Martingale Volatility of Finance Market Returns
Joseph L. McCauley
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 fluctuati…
Martingales, the Efficient Market Hypothesis, and Spurious Stylized Facts
Joseph L. McCauley, Kevin E. Bassler, Gemunu H. Gunaratne
The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts,…