The financial dynamics is a multiscale phenomenon and therefore the question which of its properties are scale invariant and which are scale characteristic refers to the essence of this phenomenon. There exists strong related evidence that at least a large portion of the financial dynamics is governed by phenomena analogous to criticality in the statistical physics sense. In its conventional form criticality implies a continuous scale invariance in terms of the standard power-law. The financial dynamics seems to be governed by a generalization of this concept such that the conventional dominating scaling acquires a correction that is periodic in the logarithm of the distance from the critical time. Such points coincide thus with the accumulation of oscillations and it is this effect that can potentially be used for prediction. An important related element, for a proper interpretation and handling of the financial patterns, as well as for consistency of the theory, is that such log-periodic patterns manifest their action self-similarly for various time-scales. This applies both to the accelerating bubble and to the decelerating anti-bubble market phases. Another crucial element is identification that the preferred scaling factor is the same through all the time scales and markets. This fact significantly amplifies the predictive power of the corresponding methodology as compared to other methods presented so far in the literature. We provide several further and more recent examples of the financial dynamics from several markets all around the world that can consistently be decomposed into quite transparent log-periodic components. Guided by the corresponding methodology we design some forecasting scenarios for the world stock market future developments.

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