To LittleTiger
So a critical point is like the Reynolds number that governs the phase change between laminar flow and turbulence? This is different from the “critical state” in my 4-state model. Consider in general the stock market have many states (e.g., overbought [OB], oversold [OS], bullish rally [BR], bearish sell off [BSO], range bounded [RB], within an up / down channel [UC, DC]), and one can come up with a Markov model to describe the (random) transition among those states. So the market could be in overbought [OB] state today, and it has 80% probability to exit overbought state (that means it could be in one of the following states: oversold [OS], bullish rally [BR], bearish sell off [BSO], range bounded [RB], within an up / down channel [UC, DC]) tomorrow, and another 20% probability to stay in overbought [OB] state tomorrow. In normal cases, the number of next possible states is large and probability is evenly distributed among those states, which makes prediction very hard. For example, suppose today the market is in [OB], and from [OB], the market can move to 6 different states (OS, BR, BSO, RB, UC, DC), each with probability 1/6. So what would be tomorrow’s state? Well, it’s hard to say because there are so many possibilities and all of them are equally probable. Those states are called “non-critical state”. Now, suppose some states, those “critical state”, have smaller number of next states and the probability distribution highly favors even fewer states. For example, when the market is oversold and VIX spike, with 90% probability it will rebound the next day. Those “critical states” make prediction much easier. My example may give you impression that “critical state” is equivalent to “critical point”, which are likely to introduce phase change (from oversold to rebound). However, a critical state doesn’t necessary mean that the market is at extreme or a phase change will show up. For another example, if a major resistance is broken, and VIX stays low, then with high probability the current trend will continue. This is also a “critical state”, because it’s easy to predict the future movement (trend continues). However, there is no phase change involved as the trend continues. |