  Taylor's power law (or fluctuation scaling) states that on comparable
populations, the variance of each sample is approximately proportional to a
power of the mean of the population. It has been shown to hold by empirical
observations in a broad class of disciplines including demography, biology,
economics, physics and mathematics.
  In particular, it has been observed in the problems involving population
dynamics, market trading, thermodynamics and number theory.
  For this many authors consider panel data in order to obtain laws of large
numbers and the possibility to fit those expressions; essentially we aim at
considering ergodic behaviors without independence. Thus we restrict the study
to stationary time series and we develop different Taylor exponents in this
setting.
  From a theoretic point of view, there has been a growing interest on the
study of the behavior of such a phenomenon. Most of these works focused on the
so-called static Taylor related to independent samples. In this paper, we
introduce a dynamic Taylor's law for dependent samples using self-normalised
expressions involving Bernstein blocks. A central limit theorem (CLT) is proved
under either weak dependence or strong mixing assumptions for the marginal
process. The limit behavior of such a new index involves the series of
covariances unlike the classic framework where the limit behavior involves the
marginal variance. We also provide an asymptotic result for for a
goodness-of-fit testing suited to check whether the corresponding dynamical
Taylor's law holds in empirical studies. Moreover, we also obtain a consistent
estimation of the Taylor's exponent.
