Eyeballing is enough to conclude this is not random. e.g. after 6 down days, the next one was always up. And after 2 down days the next day has significantly more than its fair share of ups.
A different story for up days which managed far more longer runs.
Hence Dow closes are demonstrably reasonably predictable - i.e. not random.
Can those of you claiming otherwise provide evidence to support your assertions?
A more useful exercise I've been conducting privately is to smooth out share movements, approximating them by swings of )say) 25% ups (balanced by 20% downs). e.g. only registering an upswing when a 25% gain is reached or surpassed. I found that resultant movements of individual shares were far from random and thus debunked the lame hypotheses that helped Black and Scholes win a Nobel Prize for their now totally discredited method.