# Why does the 1st derivative appear to lag the slope of the fit in Scipy's Savitzky-Golay filter?

I have a simple script that performs the Savitzky-Golay filter on a toy dataset of forex prices from yahoo finance:

import scipy.signal

splinal_fit = scipy.signal.savgol_filter(price_series, window_length=21, polyorder=2, deriv=0, mode='mirror')
splinal_fit = pandas.Series(splinal_fit, index=price_series.index, name='fit')
splinal_deriv = scipy.signal.savgol_filter(price_series, window_length=21, polyorder=2, deriv=1, axis=0, delta=1)
splinal_deriv = pandas.Series(splinal_deriv, index=price_series.index, name='fit')


The fit and derivatives looks broadly sensible, however, the x-axis seems skewed. Here is what I ran to plot the derivative alongside the original fit:

import matplotlib.pyplot as plt

mask = ((price_series.index < '2014-02-28') & (price_series.index >= '2014-02-01'))
fig, [ax1, ax2] = plt.subplots(2, 1, sharex = True, figsize=(5,10))

plt.grid(visible=True)

ax1.grid(visible=True)
ax2.grid(visible=True)


Output:

I've circled the points at which the slope of the fit appears zero, and where the derivative sign flips. However, contrary to my expectation, these don't line up. They're off by about 1-2 days. Why is this happening?

Also, the derivative on the 24th of February appears slightly positive, whereas the slope of the fit is still clearly descending. What am I missing here?

This is more of a guess than an answer, but I think the deriv parameter is used to analytically deduce the nth order derivative of the polynomial used to fit each point.

Since each point is a separate fit, the derivative of the line created by the individual fit points at independent variable x isn't necessarily the same as the nth order derivative calculated at x for the polynomial calculated for point x.

This explains why the derivative is almost the same, since you'd expect neighbouring polynomial regressions to have roughly similar slopes.