Dara wrote:

> According to Mathematicaâ€™s Correlation function:

> [Correlation](http://reference.wolfram.com/language/ref/Correlation.html)

Okay, the "details" here say Correlation computes [Pearson's correlation coefficient](https://en.wikipedia.org/wiki/Pearson%27s_correlation_coefficient#Definition), which seem to be exactly the same as what I was calling the [normalized cross-correlation](https://en.wikipedia.org/wiki/Cross-correlation#Normalized_cross-correlation).

Namely, for two lists of numbers $v_i$, $w_i$ with the same length, this is

$$ \frac{\langle v w \rangle \;-\; \langle v \rangle \langle w \rangle}{sd(v) \; sd(w) } $$

where $\langle \rangle $ means 'mean' and $sd$ means 'standard deviation'.

> Raw data correlation between Tahiti and Darwin data is 0.583649

That's impossible with the definition I just gave! You can just look: the correlation has to be negative, because the blue curve here tends to be above zero when the red one is below zero, and vice versa:

So, there is some mistake somewhere.

> According to Mathematicaâ€™s Correlation function:

> [Correlation](http://reference.wolfram.com/language/ref/Correlation.html)

Okay, the "details" here say Correlation computes [Pearson's correlation coefficient](https://en.wikipedia.org/wiki/Pearson%27s_correlation_coefficient#Definition), which seem to be exactly the same as what I was calling the [normalized cross-correlation](https://en.wikipedia.org/wiki/Cross-correlation#Normalized_cross-correlation).

Namely, for two lists of numbers $v_i$, $w_i$ with the same length, this is

$$ \frac{\langle v w \rangle \;-\; \langle v \rangle \langle w \rangle}{sd(v) \; sd(w) } $$

where $\langle \rangle $ means 'mean' and $sd$ means 'standard deviation'.

> Raw data correlation between Tahiti and Darwin data is 0.583649

That's impossible with the definition I just gave! You can just look: the correlation has to be negative, because the blue curve here tends to be above zero when the red one is below zero, and vice versa:

So, there is some mistake somewhere.