Analyzing US Inflation 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['infl'].plot()
plt.ylabel("infl")

Text(0, 0.5, 'infl')

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

# unpacking
infl_cycle, infl_trend = sm.tsa.filters.hpfilter(df.infl)

infl_cycle

1959-03-31    -1.206811
1959-06-30     1.141499
1959-09-30     1.550564
1959-12-31    -0.909577
1960-03-31     1.140149
                ...    
2008-09-30    -5.064733
2008-12-31   -10.550048
2009-03-31    -0.681429
2009-06-30     1.883255
2009-09-30     2.206560
Name: infl, Length: 203, dtype: float64

type(infl_cycle)

pandas.core.series.Series

df["trend"] = infl_trend

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

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

<matplotlib.axes._subplots.AxesSubplot at 0x7fec38616be0>