Compute percentage change by increasing window size up to period

Say I have this series

s = pd.Series([90, 91, 85, 95])

If I compute the percentage change with a period of 2 I get

s.pct_change(periods=2)

0         NaN
1         NaN
2   -0.055556
3    0.043956
dtype: float64

But say I have a couple of years of data and I want to compute the year over year (YoY) rolling returns, with pct_change(365). Then I would loose a year's worth of data (in the sense that I have 365 NaN values before I have a valid observation).

I would instead like to compromise by starting as if I had a period of 1, 2, then 3 and so on up until I reach the specified periods.

In other words, I would like an output of the likes of

0         NaN
1    0.011111
2   -0.055556
3    0.043956
dtype: float64

or

0           0
1    0.011111
2   -0.055556
3    0.043956
dtype: float64

Is this possible? I know that pandas.DataFrame.rolling has basically this functionality with the argument min_periods, but I couldn't find something similar for pandas.DataFrame.pct_change.

You can use [tag:numpy] and its sliding_window_view:

from numpy.lib.stride_tricks import sliding_window_view as swv

N = 2

v = swv(np.pad(s, (N, 0), constant_values=s.iloc[0]), N+1)

out = pd.Series((v[:, -1]-v[:, 0])/v[:, 0], index=s.index)

Output:

0    0.000000
1    0.011111
2   -0.055556
3    0.043956
dtype: float64

With pandas, it looks like a rolling in which you use the first and last value of the window:

N = 2

s.rolling(N+1, min_periods=0).apply(lambda x: (x.iloc[-1]-x.iloc[0])/x.iloc[0])

Output:

0    0.000000
1    0.011111
2   -0.055556
3    0.043956
dtype: float64