Asymmetry in power-law magnitude correlations

Time series of increments can be created in a number of different ways from a variety of physical phenomena. For example, in the phenomenon of volatility clustering-well-known in finance-magnitudes of adjacent increments are correlated. Moreover, in some time series, magnitude correlations display asymmetry with respect to an increment's sign: the magnitude of |x_{i}| depends on the sign of the previous increment x_{i-1} . Here we define a model-independent test to measure the statistical significance of any observed asymmetry. We propose a simple stochastic process characterized by a an asymmetry parameter lambda and a method for estimating lambda . We illustrate both the test and process by analyzing physiological data.