Analyzing US Unemployment From 1959 - 2009 with statsmodels

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.macrodata.load_pandas().data

print(sm.datasets.macrodata.NOTE)

::
    Number of Observations - 203

    Number of Variables - 14

    Variable name definitions::

        year      - 1959q1 - 2009q3
        quarter   - 1-4
        realgdp   - Real gross domestic product (Bil. of chained 2005 US$,
                    seasonally adjusted annual rate)
        realcons  - Real personal consumption expenditures (Bil. of chained
                    2005 US$, seasonally adjusted annual rate)
        realinv   - Real gross private domestic investment (Bil. of chained
                    2005 US$, seasonally adjusted annual rate)
        realgovt  - Real federal consumption expenditures & gross investment
                    (Bil. of chained 2005 US$, seasonally adjusted annual rate)
        realdpi   - Real private disposable income (Bil. of chained 2005
                    US$, seasonally adjusted annual rate)
        cpi       - End of the quarter consumer price index for all urban
                    consumers: all items (1982-84 = 100, seasonally adjusted).
        m1        - End of the quarter M1 nominal money stock (Seasonally
                    adjusted)
        tbilrate  - Quarterly monthly average of the monthly 3-month
                    treasury bill: secondary market rate
        unemp     - Seasonally adjusted unemployment rate (%)
        pop       - End of the quarter total population: all ages incl. armed
                    forces over seas
        infl      - Inflation rate (ln(cpi_{t}/cpi_{t-1}) * 400)
        realint   - Real interest rate (tbilrate - infl)

df.head()

	year	quarter	realgdp	realcons	realinv	realgovt	realdpi	cpi	m1	tbilrate	unemp	pop	infl	realint
0	1959.0	1.0	2710.349	1707.4	286.898	470.045	1886.9	28.98	139.7	2.82	5.8	177.146	0.00	0.00
1	1959.0	2.0	2778.801	1733.7	310.859	481.301	1919.7	29.15	141.7	3.08	5.1	177.830	2.34	0.74
2	1959.0	3.0	2775.488	1751.8	289.226	491.260	1916.4	29.35	140.5	3.82	5.3	178.657	2.74	1.09
3	1959.0	4.0	2785.204	1753.7	299.356	484.052	1931.3	29.37	140.0	4.33	5.6	179.386	0.27	4.06
4	1960.0	1.0	2847.699	1770.5	331.722	462.199	1955.5	29.54	139.6	3.50	5.2	180.007	2.31	1.19

index = pd.Index(sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3'))
df.index = index
df.head()

	year	quarter	realgdp	realcons	realinv	realgovt	realdpi	cpi	m1	tbilrate	unemp	pop	infl	realint
1959-03-31	1959.0	1.0	2710.349	1707.4	286.898	470.045	1886.9	28.98	139.7	2.82	5.8	177.146	0.00	0.00
1959-06-30	1959.0	2.0	2778.801	1733.7	310.859	481.301	1919.7	29.15	141.7	3.08	5.1	177.830	2.34	0.74
1959-09-30	1959.0	3.0	2775.488	1751.8	289.226	491.260	1916.4	29.35	140.5	3.82	5.3	178.657	2.74	1.09
1959-12-31	1959.0	4.0	2785.204	1753.7	299.356	484.052	1931.3	29.37	140.0	4.33	5.6	179.386	0.27	4.06
1960-03-31	1960.0	1.0	2847.699	1770.5	331.722	462.199	1955.5	29.54	139.6	3.50	5.2	180.007	2.31	1.19

df['unemp'].plot()
plt.ylabel("unemp")

Text(0, 0.5, 'unemp')

$\min_{\\{ \tau_{t}\\} }\sum_{t}^{T}\zeta_{t}^{2}+\lambda\sum_{t=1}^{T}\left[\left(\tau_{t}-\tau_{t-1}\right)-\left(\tau_{t-1}-\tau_{t-2}\right)\right]^{2}$

# unpacking
unemp_cycle, unemp_trend = sm.tsa.filters.hpfilter(df.unemp)

unemp_cycle

1959-03-31    0.011338
1959-06-30   -0.702548
1959-09-30   -0.516441
1959-12-31   -0.229910
1960-03-31   -0.642198
                ...   
2008-09-30   -0.481666
2008-12-31    0.198598
2009-03-31    1.171440
2009-06-30    2.040247
2009-09-30    2.207674
Name: unemp, Length: 203, dtype: float64

type(unemp_cycle)

pandas.core.series.Series

df["trend"] = unemp_trend

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

df[['trend','unemp']]["2000-03-31":].plot(figsize = (12, 8))

<matplotlib.axes._subplots.AxesSubplot at 0x7fdb5c2ecdd8>