How will you be able to determine whether the series posted are random?
A computer program
Do you think that markets are random?
"A random process is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution.
"
http://en.wikipedia.org/wiki/Randomness
To be very pedantic and look at the most isolated events in the universe yes because of the quantum uncertainty related to everything that happens.
On a more realistic scale if you were to say that knowing that something will happen with 99.999999999% probability is basically certain then I don't think it would be of any benefit to look for a model to explain the markets in terms of determinism since a much easier model would involve simply understanding the probability distribution of events and letting the law of large numbers take effect.
It would be simply impossible for one individual have access to all the information required to make deterministic predictions about the market not only because there is so much of it but because it is the interest of people to guard that information themselves.
Do you think that markets follow a normal distribution?
Empirically no. Events like crashes and huge periods of volatility happen more often than you would expect in a normal distribution.
Benoît Mandelbrot did some work on this:
"Mandelbrot found that price changes in financial markets did not follow a Gaussian distribution, but rather other Lévy stable distributions, having theoretically infinite variance. He found, for example, that cotton prices followed a Lévy stable distribution with parameter α equal to 1.7, rather than 2 as in a Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter."
http://en.wikipedia.org/wiki/Benoît_Mandelbrot