Time series analysis of GDP scaling and dynamical regimes

It is known the GDP of the largest ~25 economies (nations, EU) follows a power law GDP ~ 1/rank. We consider empirically observed GDP scaling over time, finding stable regimes including a high-end power law tail, a middle scaling region where GDP decreases exponentially with rank, and a more rapidly decaying low-end tail, exponentially with rank squared, over the 40 year period from 1980 to date. We create an inter-temporal surface across time, and track displacement over time of individual countries with respect to development variables. We cluster possibly related development variables relative to movement across and within scaling regimes, and test hypotheses with respect to shape of curve over time and trends of movement on curves across nations across time. We develop tests relative to hypotheses of tripartite scaling division given path of break point and change of parameters (including scaling coefficients and intercept) relative to log-normal hypotheses, including non-parametric cumulative distributional and maximum entropy tests, consider correlation across time relative to Kolmogorov-Smirnov tests, and consider empirical dynamical modeling considering deterministic chaos across lags and nonlinear causation among GDP and related development variable combinations.