Quote from kjkent1:
Your comment captures my position, but your postulate re vectors goes one step too far. If
trendlines can be extrapolated beyond their endpoints, then the same math that you would use to
predict market direction could be used to predict other natural events.
But, prediction of future (random) events violates causality and is therefore not possible. There is
no statistical means of predicting market direction based on no information other than price. It is
impossible.
Just a response to this last paragraph ... as for the rest, I enjoyed your discussion very much.
I think that market events are a subset of the class of natural events. From that you can probably
tell I'm not a dualist.
Of course, not all classes of natural events are easily predictable ... this is why people have
invented the notion of randomness in the first place. Randomness is not an easy concept to define
precisely, but it's fairly clear from ordinary usage that what people mean by saying that some
events are random is that some events are very hard, even impossible, to predict.
Laplace famously claimed that if the current state of the whole world could be known with exact
precision, then its future state could be predicted with exact precision. If this point of view were
correct there would be, in a strict sense, no such thing as a random event, given that the world had
some precise initial state. But it's perfectly clear that even if we did know the current state of
the world with exact precision, no one, including Laplace, could ever hope to solve the equations
that determine its future state.
So clearly there remain natural events which are for all intents and purposes impossible to predict,
and people can then usefully call such events `random.' But it's also clear that there is a
continuum between random and predictable when it comes to characterizing natural events: these are
not black and white categories.
The interesting question for traders is where do market events lie on that spectrum. If market
events are truly random then it is clearly hopeless to expect to do any better than average in the
long run.
Laplace's notion has been called causal determinism. It's a strict property of the physical theory
he was discussing: classical mechanics. Causal determinism also implies the statement that a cause
always precedes its effect, which is what people often mean when they refer simply to `causality.'
Modern physics had to drop this simple notion of causality, since the whole idea that one event
precedes another turned out to be dependent on the motion of the observer. But it was replaced by a
notion that a cause must precede its effect according to all inertial observers, in special
relativity, or that a cause must lie in the past light cone of its effect, in general relativity. This
definition allows for a strict local ordering of events and a division of events into future and
past.
Prediction of future (random) events in a statistical sense does not violate causality defined in
that way. What would violate causality is if events in the local future could affect events in the
local past.
Quantum mechanics is a theory which applies to natural events on very small length scales, and it is
a physical theory which precisely predicts the expected probability distributions for microscopic
events. Many microscopic events do appear to occur randomly when observed on an individual
basis. But when large numbers of such events are observed, quantum mechanics makes definite and
successful predictions about such events in a statistical sense. The behaviour of quantum mechanical
probability distributions between measurements is perfectly causal and the time evolution is
completely determined, given that the same initial conditions apply.
So there is an existence proof: it's a case in which there is no violation of causality implied
simply because people can and do can make statistical predictions about random future events.
The empirical evidence, inconclusive as it is, seems to me to run somewhat counter to the idea that
price series are essentially random with possibly some long term drift in prices either up or down.
The odd thing is that historical time series of prices generally exhibit non-trivial
autocorrelation. This does suggest that the price series are not generated by Markov processes,
though of course it doesn't prove it, since we do not know the future behaviour. It's certainly easy
to give a time series which appears to be predictable up to step i, for which the predictability
breaks down at step i+1. For any finite series, one can never distinguish which of the two cases one
has (predictable or not).
If one truly believed that price series were Markovian, there would be no justification for trading.
It's not what I believe, but I can't prove that what I believe is right, and I seem to have no
better than 50/50 predictive ability in practice, so I don't want to make a very strong point out of
any of this.