/ TIMESERIES

Time Series Analysis - Time Series Analysis with Statsmodels

Time Series Analysis with Statsmodels

import numpy as np
import pandas as pd
%matplotlib inline

import matplotlib.pyplot as plt

df = pd.read_csv('Data/macrodata.csv', index_col = 0, parse_dates = True)

df.head()
year quarter realgdp realcons realinv realgovt realdpi cpi m1 tbilrate unemp pop infl realint
1959-03-31 1959 1 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 2 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 3 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 4 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 1 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['realgdp'].plot(figsize =(12,5))

<AxesSubplot:>

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from statsmodels.tsa.filters.hp_filter import hpfilter

gdp_cycle, gdp_trend = hpfilter(df['realgdp'])

type(gdp_trend)

pandas.core.series.Series

df['trend'] = gdp_trend

df.head()
year quarter realgdp realcons realinv realgovt realdpi cpi m1 tbilrate unemp pop infl realint trend
1959-03-31 1959 1 2710.349 1707.4 286.898 470.045 1886.9 28.98 139.7 2.82 5.8 177.146 0.00 0.00 2670.837085
1959-06-30 1959 2 2778.801 1733.7 310.859 481.301 1919.7 29.15 141.7 3.08 5.1 177.830 2.34 0.74 2698.712468
1959-09-30 1959 3 2775.488 1751.8 289.226 491.260 1916.4 29.35 140.5 3.82 5.3 178.657 2.74 1.09 2726.612545
1959-12-31 1959 4 2785.204 1753.7 299.356 484.052 1931.3 29.37 140.0 4.33 5.6 179.386 0.27 4.06 2754.612067
1960-03-31 1960 1 2847.699 1770.5 331.722 462.199 1955.5 29.54 139.6 3.50 5.2 180.007 2.31 1.19 2782.816333 
df[['trend','realgdp']]['2005-01-01':].plot(figsize = (12, 5))

<AxesSubplot:>

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ETS Models

airline = pd.read_csv('Data/airline_passengers.csv', index_col = 'Month', parse_dates=True)

airline = airline.dropna()

airline.head()
Thousands of Passengers
Month
1949-01-01 112
1949-02-01 118
1949-03-01 132
1949-04-01 129
1949-05-01 121 
airline.plot()

<AxesSubplot:xlabel='Month'>

png

from statsmodels.tsa.seasonal import seasonal_decompose

result = seasonal_decompose(airline['Thousands of Passengers'], model='multiplicative')

from pylab import rcParams
rcParams['figure.figsize'] = 12,5

result.plot();

png

EWMA Models

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

airline = pd.read_csv('Data/airline_passengers.csv', index_col="Month")

airline.dropna(inplace=True)

airline.index = pd.to_datetime(airline.index)

airline.index

DatetimeIndex(['1949-01-01', '1949-02-01', '1949-03-01', '1949-04-01',
               '1949-05-01', '1949-06-01', '1949-07-01', '1949-08-01',
               '1949-09-01', '1949-10-01',
               ...
               '1960-03-01', '1960-04-01', '1960-05-01', '1960-06-01',
               '1960-07-01', '1960-08-01', '1960-09-01', '1960-10-01',
               '1960-11-01', '1960-12-01'],
              dtype='datetime64[ns]', name='Month', length=144, freq=None)

airline.head()
Thousands of Passengers
Month
1949-01-01 112
1949-02-01 118
1949-03-01 132
1949-04-01 129
1949-05-01 121 
airline['6-month-SMA'] = airline['Thousands of Passengers'].rolling(window=6).mean()

airline['12-month-SMA'] = airline['Thousands of Passengers'].rolling(window=12).mean()

airline.plot(figsize = (10, 8));

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airline['1959':].plot();

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airline['EWMA-12'] = airline['Thousands of Passengers'].ewm(span = 12).mean()

airline[['Thousands of Passengers','EWMA-12']].plot(figsize = (10, 8))

<AxesSubplot:xlabel='Month'>

png

Holt - Winters Methods

import numpy as np
import pandas as pd
%matplotlib inline

df = pd.read_csv('Data/airline_passengers.csv', index_col = 'Month', parse_dates=True)

df = df.dropna()

df.index

DatetimeIndex(['1949-01-01', '1949-02-01', '1949-03-01', '1949-04-01',
               '1949-05-01', '1949-06-01', '1949-07-01', '1949-08-01',
               '1949-09-01', '1949-10-01',
               ...
               '1960-03-01', '1960-04-01', '1960-05-01', '1960-06-01',
               '1960-07-01', '1960-08-01', '1960-09-01', '1960-10-01',
               '1960-11-01', '1960-12-01'],
              dtype='datetime64[ns]', name='Month', length=144, freq=None)

df.index.freq = 'MS'

df.index

DatetimeIndex(['1949-01-01', '1949-02-01', '1949-03-01', '1949-04-01',
               '1949-05-01', '1949-06-01', '1949-07-01', '1949-08-01',
               '1949-09-01', '1949-10-01',
               ...
               '1960-03-01', '1960-04-01', '1960-05-01', '1960-06-01',
               '1960-07-01', '1960-08-01', '1960-09-01', '1960-10-01',
               '1960-11-01', '1960-12-01'],
              dtype='datetime64[ns]', name='Month', length=144, freq='MS')

df.head()
Thousands of Passengers
Month
1949-01-01 112
1949-02-01 118
1949-03-01 132
1949-04-01 129
1949-05-01 121 
from statsmodels.tsa.holtwinters import SimpleExpSmoothing

span = 12
alpha = 2/(span+1)

df['EWMA12'] = df['Thousands of Passengers'].ewm(alpha = alpha, adjust = False).mean()

df.head()
Thousands of Passengers EWMA12
Month
1949-01-01 112 112.000000
1949-02-01 118 112.923077
1949-03-01 132 115.857988
1949-04-01 129 117.879836
1949-05-01 121 118.359861 
model = SimpleExpSmoothing(df['Thousands of Passengers'])

C:\Users\ilvna\.conda\envs\tf-2.3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:429: FutureWarning: After 0.13 initialization must be handled at model creation
  FutureWarning,

fitted_model = model.fit(smoothing_level=alpha, optimized=False)

df['SES12'] = fitted_model.fittedvalues.shift(-1)

df.head()
Thousands of Passengers EWMA12 SES12
Month
1949-01-01 112 112.000000 112.000000
1949-02-01 118 112.923077 112.923077
1949-03-01 132 115.857988 115.857988
1949-04-01 129 117.879836 117.879836
1949-05-01 121 118.359861 118.359861 
# df['SES12'] = SimpleExpSmoothing(df['Thousands of Passengers']).fit(smoothing_level=alpha, optimized=False).fittedvalues.shift(-1)

from statsmodels.tsa.holtwinters import ExponentialSmoothing

df.plot()

<AxesSubplot:xlabel='Month'>

png

df['DES_add_12'] = ExponentialSmoothing(df['Thousands of Passengers'],trend='add').fit().fittedvalues.shift(-1)

C:\Users\ilvna\.conda\envs\tf-2.3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:429: FutureWarning: After 0.13 initialization must be handled at model creation
  FutureWarning,

df['DES_mul_12'] = ExponentialSmoothing(df['Thousands of Passengers'],trend='mul').fit().fittedvalues.shift(-1)

C:\Users\ilvna\.conda\envs\tf-2.3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:429: FutureWarning: After 0.13 initialization must be handled at model creation
  FutureWarning,

df.head()
Thousands of Passengers EWMA12 SES12 DES_add_12 DES_mul_12
Month
1949-01-01 112 112.000000 112.000000 114.221156 112.688538
1949-02-01 118 112.923077 112.923077 120.175837 118.725424
1949-03-01 132 115.857988 115.857988 134.115056 132.811491
1949-04-01 129 117.879836 117.879836 131.244976 129.793048
1949-05-01 121 118.359861 118.359861 123.283465 121.743867 
df[['Thousands of Passengers', 'SES12', 'DES_add_12','DES_mul_12']].iloc[:24].plot(figsize=(12,5))

<AxesSubplot:xlabel='Month'>

png

df['TES_mul_12']=ExponentialSmoothing(df['Thousands of Passengers'],trend='mul',seasonal='mul',seasonal_periods=12).fit().fittedvalues

C:\Users\ilvna\.conda\envs\tf-2.3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:429: FutureWarning: After 0.13 initialization must be handled at model creation
  FutureWarning,
C:\Users\ilvna\.conda\envs\tf-2.3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:80: RuntimeWarning: overflow encountered in matmul
  return err.T @ err

df.plot()

<AxesSubplot:xlabel='Month'>

png

df.columns

Index(['Thousands of Passengers', 'EWMA12', 'SES12', 'DES_add_12',
       'DES_mul_12', 'TES_mul_12'],
      dtype='object')

df[['Thousands of Passengers', 'DES_mul_12', 'TES_mul_12']].plot(figsize=(12,6))

<AxesSubplot:xlabel='Month'>

png

df[['Thousands of Passengers', 'DES_mul_12', 'TES_mul_12']].iloc[-24:].plot(figsize=(12,6))

<AxesSubplot:xlabel='Month'>

png