This post includes code adapted from python for finance and trading algorithms udemy course and python for finance and trading algorithms udemy course notebooks.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import statsmodels.api as sm
%matplotlib inline


df = sm.datasets.longley.load_pandas().data

#print(sm.datasets.longley.NOTE)

df.head()
TOTEMP GNPDEFL GNP UNEMP ARMED POP YEAR
0 60323.0 83.0 234289.0 2356.0 1590.0 107608.0 1947.0
1 61122.0 88.5 259426.0 2325.0 1456.0 108632.0 1948.0
2 60171.0 88.2 258054.0 3682.0 1616.0 109773.0 1949.0
3 61187.0 89.5 284599.0 3351.0 1650.0 110929.0 1950.0
4 63221.0 96.2 328975.0 2099.0 3099.0 112075.0 1951.0 
index = pd.Index(sm.tsa.datetools.dates_from_range('1947', '1962'))
df.index = index
df.head()
TOTEMP GNPDEFL GNP UNEMP ARMED POP YEAR
1947-12-31 60323.0 83.0 234289.0 2356.0 1590.0 107608.0 1947.0
1948-12-31 61122.0 88.5 259426.0 2325.0 1456.0 108632.0 1948.0
1949-12-31 60171.0 88.2 258054.0 3682.0 1616.0 109773.0 1949.0
1950-12-31 61187.0 89.5 284599.0 3351.0 1650.0 110929.0 1950.0
1951-12-31 63221.0 96.2 328975.0 2099.0 3099.0 112075.0 1951.0 
df['ARMED'].plot()
plt.ylabel("ARMED")

Text(0, 0.5, 'ARMED')
# unpacking
cycle, trend = sm.tsa.filters.hpfilter(df.ARMED)

cycle

1947-12-31    -497.642333
1948-12-31    -713.661033
1949-12-31    -635.368706
1950-12-31    -682.008289
1951-12-31     688.574390
1952-12-31    1108.959755
1953-12-31     992.297873
1954-12-31     731.045710
1955-12-31     370.040046
1956-12-31     124.660757
1957-12-31      15.056446
1958-12-31    -193.702199
1959-12-31    -324.553899
1960-12-31    -407.316313
1961-12-31    -393.604252
1962-12-31    -182.777954
Name: ARMED, dtype: float64
type(cycle)

pandas.core.series.Series
df["trend"] = trend

df[['trend','ARMED']].plot(figsize = (12, 8))

df[['trend','ARMED']]["1950-01-01":"1955-01-01"].plot(figsize = (12, 8))

<matplotlib.axes._subplots.AxesSubplot at 0x7f2d5af13940>