Calculating Autocorrelation of Pandas DataFrame along each Column

Question

I want to calculate the autocorrelation coefficients of lag length one among columns of a Pandas DataFrame. A snippet of my data is:

            RF        PC         C         D        PN        DN         P
year                                                                      
1890       NaN       NaN       NaN       NaN       NaN       NaN       NaN
1891 -0.028470 -0.052632  0.042254  0.081818 -0.045541  0.047619 -0.016974
1892 -0.249084  0.000000  0.027027  0.067227  0.099404  0.045455  0.122337
1893  0.653659  0.000000  0.000000  0.039370 -0.135624  0.043478 -0.142062

Along year, I want to calculate autocorrelations of lag one for each column (RF, PC, etc…).

To calculate the autocorrelations, I extracted two time series for each column whose start and end data differed by one year and then calculated correlation coefficients with numpy.corrcoef.

For example, I wrote:

numpy.corrcoef(data[['C']][1:-1],data[['C']][2:])

(the entire DataFrame is called data).
However, the command unfortunately returned:

array([[ nan,  nan,  nan, ...,  nan,  nan,  nan],
       [ nan,  nan,  nan, ...,  nan,  nan,  nan],
       [ nan,  nan,  nan, ...,  nan,  nan,  nan],
       ..., 
       [ nan,  nan,  nan, ...,  nan,  nan,  nan],
       [ nan,  nan,  nan, ...,  nan,  nan,  nan],
       [ nan,  nan,  nan, ...,  nan,  nan,  nan]])

Can somebody kindly advise me on how to calculate autocorrelations?

Asked By: fabian

||

Source

Answer 1

you should use:

numpy.corrcoef(df['C'][1:-1], df['C'][2:])

df[['C']] represents a dataframe with only one column, while df['C'] is a series containing the values in your C column.

Answered By: joaquin

Answer 2

This is a late answer, but for future users, you can also use the pandas.Series.autocorr(), which calculates lag-N (default=1) autocorrelation on Series:

df['C'].autocorr(lag=1)

http://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.autocorr.html#pandas.Series.autocorr

Answered By: eclark

Answer 3

.autocorr applies to Series, not DataFrames. You can use .apply to apply to a DataFrame:

def df_autocorr(df, lag=1, axis=0):
    """Compute full-sample column-wise autocorrelation for a DataFrame."""
    return df.apply(lambda col: col.autocorr(lag), axis=axis)
d1 = DataFrame(np.random.randn(100, 6))

df_autocorr(d1)
Out[32]: 
0    0.141
1   -0.028
2   -0.031
3    0.114
4   -0.121
5    0.060
dtype: float64

You could also compute rolling autocorrelations with a specified window as follows (this is what .autocorr is doing under the hood):

def df_rolling_autocorr(df, window, lag=1):
    """Compute rolling column-wise autocorrelation for a DataFrame."""

    return (df.rolling(window=window)
        .corr(df.shift(lag))) # could .dropna() here

df_rolling_autocorr(d1, window=21).dropna().head()
Out[38]: 
        0      1      2      3      4      5
21 -0.173 -0.367  0.142 -0.044 -0.080  0.012
22  0.015 -0.341  0.250 -0.036  0.023 -0.012
23  0.038 -0.329  0.279 -0.026  0.075 -0.121
24 -0.025 -0.361  0.319  0.117  0.031 -0.120
25  0.119 -0.320  0.181 -0.011  0.038 -0.111

Answered By: Brad Solomon

Answer 4

As I believe the use case where we need a window corresponding to highest correlation is more common, I have added another function which returns that window length per feature.

# Find autocorrelation example.
def df_autocorr(df, lag=1, axis=0):
    """Compute full-sample column-wise autocorrelation for a DataFrame."""
    return df.apply(lambda col: col.autocorr(lag), axis=axis)

def df_rolling_autocorr(df, window, lag=1):
    """Compute rolling column-wise autocorrelation for a DataFrame."""

    return (df.rolling(window=window)
        .corr(df.shift(lag))) # could .dropna() here

def df_autocorr_highest(df, window_min, window_max, lag_f):
    """Returns a dictionary containing highest correlation coefficient wrt window length."""
    df_corrs = pd.DataFrame()
    df_corr_dict = {}
    for i in range(len(df.columns)):
        corr_init = 0
        corr_index = 0
        for j in range(window_min, window_max): 
            corr = df_rolling_autocorr(df.iloc[:,i], window=j, lag=lag_f).dropna().mean()
            if corr > corr_init:
                corr_init = corr
                corr_index = j
        corr_label = df.columns[i] + "_corr"    
        df_corr_dict[corr_label] = [corr_init, corr_index]
    return df_corr_dict

Answered By: Mr. Panda

Calculating Autocorrelation of Pandas DataFrame along each Column

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