Cross-correlation (time-lag-correlation) with pandas?

Question

I have various time series, that I want to correlate - or rather, cross-correlate - with each other, to find out at which time lag the correlation factor is the greatest.

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Answer 1

As far as I can tell, there isn't a built in method that does exactly what you are asking. But if you look at the source code for the pandas Series method autocorr, you can see you've got the right idea:

def autocorr(self, lag=1):
    """
    Lag-N autocorrelation

    Parameters
    ----------
    lag : int, default 1
        Number of lags to apply before performing autocorrelation.

    Returns
    -------
    autocorr : float
    """
    return self.corr(self.shift(lag))

So a simple timelagged cross covariance function would be

def crosscorr(datax, datay, lag=0):
    """ Lag-N cross correlation. 
    Parameters
    ----------
    lag : int, default 0
    datax, datay : pandas.Series objects of equal length

    Returns
    ----------
    crosscorr : float
    """
    return datax.corr(datay.shift(lag))

Then if you wanted to look at the cross correlations at each month, you could do

 xcov_monthly = [crosscorr(datax, datay, lag=i) for i in range(12)]