[photon137]

Adding a common deterministic trend to two random time series does not make them correlated. Intuitively, you still cannot predict the deviation from the trend of one timeseries using the deviation from the trend of the other timeseries.

His statement (after adding the constant trend) is misleading:

"Now let’s repeat the same tests on these new series. We get surprising results: the correlation coefficient is 0.96 — a very strong unmistakable correlation"

What he's calculated is the correlation between a set of points from y_1 and y_2 - and that will be large, of course - their (deterministically increasing) means have correlation 1.

The quantity that qualifies as correlation for predictability purposes is actually the correlation between the deviations from mean.

This is all fairly clear if you use the actual formula (Pearson correlation):

E[(y_1 - mu * t)(y_2 - mu * t)] / (sigma_y1 * sigma_y2)