%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
plt.rcParams['text.usetex'] = False
import pandas
import seaborn
seaborn.set(style='ticks')

N = 370
dt = pandas.offsets.Milli(500)

x = np.random.lognormal(size=N)
timestamps = pandas.DatetimeIndex(freq=dt, start='2012-01-01', periods=N)

fig, (ax1, ax2) = plt.subplots(figsize=(12,4), nrows=2, sharex=True)
ts = pandas.TimeSeries(data=x, index=timestamps)
tsmean = pandas.expanding_mean(ts, min_periods=5)

diff = mean.diff()
diffmean = pandas.expanding_mean(diff, min_periods=5)

ax = ts.plot(ax=ax1, label='Measurements')
tsmean.plot(ax=ax1, label='Expanding Mean')
ax1.set_yscale('log')
ax1.set_ylabel('Flow velocity (m/s)')
ax1.xaxis.tick_top()

diff.plot(ax=ax2)
diffmean.plot(ax=ax2)
ax2.set_ylabel('Diff of mean velocity')

ax1.legend(ncol=2, loc='lower right')

seaborn.despine(ax=ax1, bottom=True, top=False)
seaborn.despine(ax=ax2, bottom=False, top=True)