I have a pandas dataframe and I am trying to estimate a new timeseries V(t) based on the values of an existing timeseries B(t). I have written a minimal reproducible example to generate a sample dataframe as follows:

```
import pandas as pd
import numpy as np
lenb = 5000
lenv = 200
l = 5
B = pd.DataFrame({'a': np.arange(0, lenb, 1), 'b': np.arange(0, lenb, 1)},
index=pd.date_range('2022-01-01', periods=lenb, freq='2s'))
```

I want to calculate V(t) for all times ‘t’ in the timeseries B as:

```
V(t) = (B(t-2*l) + 4*B(t-l)+ 6*B(t)+ 4*B(t+l)+ 1*B(t+2*l))/16
```

How can I perform this calculation in a vectorized manner in pandas? Lets say that l=5

Would that be the correct way to do it:

```
def V_t(B, l):
V = (B.shift(-2*l) + 4*B.shift(-l) + 6*B + 4*B.shift(l) + B.shift(2*l)) / 16
return V
```

### >Solution :

I would have done it as you suggested in your latest edit. So here is an alternative to avoid having to type all the `shift`

commands for an arbitrary long list of factors/multipliers:

```
import numpy as np
def V_t(B, l):
X = [1, 4, 6, 4, 4]
Y = [-2*l, -l, 0, l, 2*l]
return pd.DataFrame(np.add.reduce([x*B.shift(y) for x, y in zip(X, Y)])/16,
index=B.index, columns=B.columns)
```