用熊猫计算Python中的考夫曼效率比？

Question

I'm trying to implement the Kaufman Efficiency Ratio (ER) in Python with Pandas.

In a Pandas DataFrame, I have two columns:

1. Date
2. Closing Price of a stock (the German DAX index, ^GDAXI, in this example):

Date        Close
    2016-01-05  10310.10
    2016-01-06  10214.02
    2016-01-07   9979.85
    2016-01-08   9849.34
    2016-01-11   9825.07     
    2016-01-12   9985.43     
    2016-01-13   9960.96     
    2016-01-14   9794.20

What I need is a third column that includes the ER for a given period n.

Definition of the ER:

ER = Direction / Volatility

Where:

Direction = ABS (Close – Close[n])
Volatility = n * ∑ (ABS(Close – Close[1]))
n = The efficiency ratio period.

Here is an example of an=3 period ER (taken from http://etfhq.com/blog/2011/02/07/kaufmans-efficiency-ratio/ ):

What I'm struggeling with is how to do this in Python with Pandas? In the end, my dataframe should look like this, according to the calculation above:

Date        Adj Close   ER(3)
2016-01-04  10283.44    
2016-01-05  10310.10    
2016-01-06  10214.02    
2016-01-07  9979.85     0.9
2016-01-08  9849.34     1.0
2016-01-11  9825.07     1.0
2016-01-12  9985.43     0.0
2016-01-13  9960.96     0.5
2016-01-14  9794.20     0.1

How do I make Pandas to look back at the previous n rows for the calculation needed for the ER?

Any help is greatly appreciated! Thank you in advance. Dirk

Answer 1

No need to write a rolling function, just use diff and rolling_sum :

df['direction'] = df['Close'].diff(3).abs()
df['volatility'] = pd.rolling_sum(df['Close'].diff().abs(), 3)

I think the code is pretty much self-explanatory. Please let me know if you would like explanations.

In [11]: df['direction'] / df['volatility']
Out[11]: 
0         NaN
1         NaN
2         NaN
3    1.000000
4    1.000000
5    0.017706
6    0.533812
7    0.087801
dtype: float64

This looks like what you're looking for.