Lag-1 autocorrelation function
        as defined in Riley 2004, Eqn (2)
        used by autocorr_noise_id()
        
        Parameters
        ----------
        x: numpy.array
            time-series
        Returns
        -------
        ACF: float
            Lag-1 autocorrelation for input time-series x
        
        Notes
        -----
        * a faster algorithm based on FFT might be better!?
        * numpy.corrcoeff() gives similar but not identical results.
            #c = np.corrcoef( np.array(x[:-lag]), np.array(x[lag:]) )
            #r1 = c[0,1] # lag-1 autocorrelation of x

def lag1_acf(x, detrend_deg=1):
    """ Lag-1 autocorrelation function
        as defined in Riley 2004, Eqn (2)
        used by autocorr_noise_id()
        
        Parameters
        ----------
        x: numpy.array
            time-series
        Returns
        -------
        ACF: float
            Lag-1 autocorrelation for input time-series x
        
        Notes
        -----
        * a faster algorithm based on FFT might be better!?
        * numpy.corrcoeff() gives similar but not identical results.
            #c = np.corrcoef( np.array(x[:-lag]), np.array(x[lag:]) )
            #r1 = c[0,1] # lag-1 autocorrelation of x
    """
    mu = np.mean(x)
    a=0
    b=0
    for n in range(len(x)-1):
        a = a + (x[n]-mu)*(x[n+1]-mu)
    for n in range(len(x)):
        b=b+pow( x[n]-mu , 2 )
    return a/b