At the risk of revisiting the recent diatribes going back and forth on random walks and the market, I would like to add an observation, fwiw.
Ahhaha is right about the market fitting a random walk model, that is, a first order markov process in discrete time (weiner process in continuous time, if you believe such a thing is possible). This is neither a new nor a particularly interesting statement.
A number of theoreticians have reached this conclusion, and it is even used as an example in the Box-Jenkins time series textbook. However, ahhaha is wrong about one important thing -- it is not the periodic market values that are best modeled by a random walk, but the residuals -- the error terms. That is also not surprising, since the residuals are the sum total of all of the buys and sells during the day, which represent the market's efficiency, and collective ignorance.
What is more significant is the long term trend, which is not best fit by a random walk, at least not in the time frames of interest. Going back for at least a century or more, the trend has been positive, with certain cycles that many have tried to decipher. This does not help the short term trader, that is, anyone with a time frame shorter than a year or so, but it is a clear enough trend that one can conclude statistically that a pure random walk model can be rejected in favor of some type of markov process with a trend (e.g., an arima model in time series terms).
I would have contributed to this discussion earlier, but chose to sit on the sideline, having been accused of being a lemon sucker or something equivalent to that in previous discussions on the matter -- I only have a doctorate in stochastic processes, and am not the only expert in the world who is qualified to speak on such heady topics -g- |
