# How to estimate the predition power of x(t) on y(t)?

Suppose I have two time series: y(t) and x(t), with y(t) the time series I want to predict and x(t) as the input for the prediction. My question is straightforward. How do I know if x(t) has the prediction power for y(t)?

I have come up with the correlation function of two kinds:

1. the python cross correlation function np.correlate. This function computes the correlation as generally defined in signal processing texts: $$c_{av}[k] = \sum_n a[n+k] * conj(v[n])$$

2. the python correlation coefficients np.corrcoef. Return Pearson product-moment correlation coefficients.

Which one is a better estimate of prediction power or represent a better correlation between the two? What is the difference between the two (of course their formula are different, but what does that represent?)

If I want to predict y(t) with a model f, which takes argument of x(t), x(t-1), etc. How many lags should I keep? Is there any method to estimate this?

Should I just calculate the np.corrcoef(y(t), x(t)) and np.corrcoef(y(t), x(t-1)) and see the decaying properties the this correlation coefficients and made a cutoff at some point? I hope you can shed some light about my concerns.