Robert Shiller’s’ Paper on ‘The Volatility of Stock markets Prices’ published in 1987 uses dividend data and real interest rates to seek evidence that true investment value changes through time sufficiently to justify the price changes. His paper concluded that most of the volatility of the stock market prices appears unexplained. Shiller volatility or fluctuations prove that behavior of markets is not normal. Non normal distribution series is a widely followed proof of inefficiency in prices.

The authors of the current paper reanalyze Shiller’s data not for the change but for rate of change. The rate of change in dividend values, interest rates and market price is used to isolate temporal changes (time durations) defined in days. Though on one side the time duration data illustrate a non normal distribution and confirms Shiller’s non normalcy finding within value (fundamental data) and market data, it opens a larger debate suggesting temporal changes to be the reason for market volatility and inefficiency.

Divergence is an understudied subject loosely defined as an unpredictable random error. The classification of divergences as small or large is also at the heart of efficient or inefficient market theory debate. This paper explains how divergence is cyclical and can be quantified and used as a predictive model.

Classic studies of the probability density of price fluctuations g for stocks and foreign exchanges of several highly developed economies have been interpreted using a power-law probability density function P(g)~g-(α1) with exponent values α>2, which are outside the Levy-stable regime 0<α<2. To test the universality of this relationship in ‘time duration,’ we isolate the time duration between rate of change for the period Jan 2000-Oct 2010 for the 23 largest stocks of the Bucharest Stock Exchange which has the highest volume of trade in Romania. We find that D(g) decays as an exponential function D(g)~exp(-βg) with a characteristic decay scales β=2.45±0.045. Thus we conclude that time duration in Romanian stock market may belong to a universality class that is witnessed in equity prices around the world.

Mandelbrot said there is no mystery but patterns. Mandelbrot developed the idea of fractals while trying to determine the length of the British coastline, when he realized a seemingly smooth shore becomes more and more detailed as you zoom in. He also described his life as a very crooked line. But despite being the inspiration for such metaphysics, Mandelbrot, when asked if fractals don’t point to a single rule underlying reality, has simply stated, “There is no single rule that governs the use of geometry. I don’t think one exists”.

Pareto could not understand why patterns of wealth allocation were disproportionate (80% of the wealth with 20% of the people). He called it the ‘wonder of men’. Edward R Dewey (Great Depression Economist under President Hoover) witnessed overwhelming connections among time cycles. He called it a mysterious force, which connects all of us.

Human study of scale invariant natural patterns invariably stops at Pareto exponentiality. US scholar Albert Bartlett pointed out the difficulty to grasp ramifications of exponential growth, stating: “The greatest shortcoming of the human race is our inability to understand the exponential function”.

This paper summarizes the philosophy of Time Topology and builds a historical and statistical case to explain that just like patterns in natural systems even Time is patterned. This on one side looks plausible but on the other leads us to a critical Cartesian debate because Time is the common (x-axis) element against all the other natural (Y- axis) systems. Patterns can’t exist on both the Cartesian levels. This would mean that either Time (the only patterned element) gives (order and disorder) pattern to all natural systems or there is some other mysterious force or just patterns and no mystery (Mandelbrot).