Consumption and Fractional Differencing: Old and New Anomalies

This paper calculates the stochastic properties of consumption when income follows a fractional stochastic process, and shows how this may explain both the excess sensitivity and the excess smoothness paradoxes. It then uses a recently developed improvement of the Rescaled Range Statistic to find long term memory in consumption. The remaining sections undertake Monte Carlo simulations to assess the finite sample size and power of the test, conduct cross country comparisons (France, Canada, U.K.), and provides a possible explanation.