Regression of a timeseries delta in pandas

Question

Lets say I have a timeseries like this

    A   B
0   a   b
1   c   d
2   e   f 
3   g   h

0,1,2,3 are times, a, c, e, g is one time series and b, d, f, h is another time series.

What i need is a regression of deltas, meaning

       dA     dB
0    (a-c)  (b-d)
1    (c-e)  (d-f)
2    (e-g)  (f-h)

I was to do regress as dB = X dA + Y

Now whats the best way to do this if i have a pandas dataframe like above to start with. Also, next I would like to do a moving window regression.

Answer 1

pandas and statsmodel work beautifully together for things like this, see this example:

In [16]:

import statsmodels.formula.api as smf
In [17]:

df=pd.DataFrame(np.random.random((10,2)), columns=['A','B'])
In [18]:

df.index=pd.date_range('1/1/2014', periods=10)
In [19]:

dfd=df.diff().dropna()
In [20]:

print df
                   A         B
2014-01-01  0.455924  0.375653
2014-01-02  0.585738  0.864693
2014-01-03  0.201121  0.640144
2014-01-04  0.685951  0.256225
2014-01-05  0.203623  0.007993
2014-01-06  0.626527  0.719438
2014-01-07  0.327197  0.324088
2014-01-08  0.115016  0.635999
2014-01-09  0.660070  0.246438
2014-01-10  0.141730  0.125918

[10 rows x 2 columns]
In [21]:

print dfd
                   A         B
2014-01-02  0.129814  0.489041
2014-01-03 -0.384617 -0.224549
2014-01-04  0.484830 -0.383919
2014-01-05 -0.482328 -0.248233
2014-01-06  0.422905  0.711446
2014-01-07 -0.299330 -0.395351
2014-01-08 -0.212182  0.311911
2014-01-09  0.545054 -0.389561
2014-01-10 -0.518340 -0.120520

[9 rows x 2 columns]
In [22]:

mod1 = smf.ols('A ~ B', data=dfd).fit()
In [23]:

print mod1.summary()
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      A   R-squared:                       0.036
Model:                            OLS   Adj. R-squared:                 -0.101
Method:                 Least Squares   F-statistic:                    0.2637
Date:                Fri, 18 Apr 2014   Prob (F-statistic):              0.623
Time:                        13:54:27   Log-Likelihood:                -4.5434
No. Observations:                   9   AIC:                             13.09
Df Residuals:                       7   BIC:                             13.48
Df Model:                           1                                         
==============================================================================
                 coef    std err          t      P>|t|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
Intercept     -0.0295      0.152     -0.194      0.852        -0.389     0.330
B              0.1960      0.382      0.513      0.623        -0.707     1.099
==============================================================================
Omnibus:                        1.832   Durbin-Watson:                   3.290
Prob(Omnibus):                  0.400   Jarque-Bera (JB):                1.006
Skew:                           0.506   Prob(JB):                        0.605
Kurtosis:                       1.711   Cond. No.                         2.52
==============================================================================

For the 2nd question you have to provide more detail or open a separate question. There are many different kinds of sliding windows, you need to be more specific.

Edit

The simple linear regression you just described, in case you only want to store the two coefficients, can be achieved as follows:

win_size=5
win_step=2
coef_ls=[]
for i in range(0,len(dfd)-win_size,2):
    coef_ls.append(smf.ols('A ~ B', data=dfd.ix[i:i+win_size]).fit().params)
pd.concat(coef_ls, axis=1).T # The resulting DataFrame of coefficients.