Wal-Mart Stores Inc
Singapore Press Holdings
Golden Agri- Resources
Genting Singapore
If stocks do have some repetition in the nature of their movements, it would still be too elusive for us to 'capture' for prediction. If patterns do exist, they are always changing. Thus, a Moving Average crossover that served you so well in the past will suddenly not work. Even so called natural phenomena like Fibonacci and Elliot Waves cannot cope with these constant changes. Yet, the changes in a stock's time series are not totally random either. Besides being underpinned by fundamentals in the long run, they also have rhythms and cycles caused by autocorrelation, their Beta, and momentum. And like all complex adaptive systems, action creates reaction, and evolution spawns co-evolution. Thus in this dynamic environment where equilibrium is a moving target, we buy and sell, attempting to impose some order on the seeming Chaos, but never quite succeeding. The reason is the great degree of non-linearity which cannot be captured by traditional statistics or any other parametric, linear approach. However, Wavelets- a technology that greatly enhances the efficiency for de-noising, compressing and analyzing 1-dimensional and 2-dimensional signals can give us an inkling of the character of a stock. For more on Wavelets see:http://www.fu-lu-shou.net/2010/10/stock-market-data-as-art.html Here we use a 1-dimensional continuous Daubechies 5 wavelet for analysing and comparing the 'predictability' of stocks. The patterns that you see in the images above are patterns of fractal self-similarity, which is something from Chaos Theory and much related to the work of Benoit Mandelebrot the mathematician who recently passed away. Books that tell the story of the great Quantitative Analysis traders who ran the proprietary trading desks of Goldman Sachs or started hedge funds show that many of them consulted Benoit Mandlebrot on aspects of Chaos Theory that could be applied to short term trading. Intuitively, when there are more distinct patterns, we can say that the stock is more predictable [at least during the period when the patterns are distinct]. Mathematically, to delve into a more quantitative analysis of predictability involves looking at the wavelets different levels, the Details amd Approximations and the coefficients.* When a signal is decomposed by stretching parts of the Mother Waevelet, to fit a particular length of signals, a 'tree' with two branches and several levels is created: Approximations for low frequencies of the signal and Details for high frequencies parts of the signal. Analysis of wavelets requires deep domain knowledge which a Wavelet novice like me do not possess. It takes years to learn to pick the right family of wavelets to apply, and it is still an art to choose the level of decomposition, and then to interpret the results. Maybe for image compression or classfication Wavelets requires less heuristics, but definitely for use of Wavelets in financial data, a person with domain knowledege of both Wavelets as well as financial markets is required.
In the images above, of some popular stocks on the Singapore Exchange, all I can conclude is that the movement is not entirely random, there is method even in the madness of a stock like Genting, and we can say that some stocks are more predictable than others. For a great contrast, look at the 'regularity' of a stock like the USA's Wal-Mart and compare it with Genting where some areas are without any patterns at all. A Blue Chip like Singapore Press Holdings bears some resemblance to Wal Mart in behavior. Golden Agri and Yangzijiang look frightening. The fine details at the bottom of both show very short buying and selling 'cycles' as in contra trades.
