FR2215: L4 (Regression Model)

statsmodel library

library for estimating statistical models

importing statsmodel

import statsmodel

import statsmodel.formula.api as smf (specifying models from pandas df)

from statsmodels.tsa.ar_model import AutoReg

scikit-learn library

library for machine learning tools

importing scikit-learn

import sklearn

from sklearn.linear_model import LinearRegression

declaring data as time-series

df[‘x’] = pd.to_datetime(df[‘x’])

• do this prior to setting date as the index bc python will no longer recognize it as a column

mean reverting

deviations from the avg are expected to reverse, return to avg over time

what do to if time series variable is non mean reverting

work w/ the variable's differences

2 mean reversion tests

1. ADF

2. KPSS

ADF test

• not robust

• suboptimal test

• good in periods of calm markets

• Ho: has a unit root, Ha: has no unit root

  • rejecting null provides evidence supporting non-stationarity

robust

produces reliable results even w/ outliers and violated assumptions

KPSS test

• robust

• optimal

• Ho: trend stationary, Ha: has a unit root (not trend stationary)

generating variable differences

∆G_T = G_T - G_T-1

generating variable differences in python

df2 = df.set_index(‘Date’).diff().reset_index()

• 1st element becomes unavailable bc no differences

• df.dropna() for NaNs

descriptive stats on python

• df.describe()

• df.corr()

correlation

measure of linear dependence

• most financial variables are non-linearly dependent

correlation threshold to run a regression

0.5

skew

measure of asymmetry around the mean

• x = df[‘x’].skew() (n/a for time series)

kurtosis

measure of tail fatmess

• x = df[‘x’].kurt()

testing for mean reversion steps

1. mean reversion test (KPSS then ADF)

2. transform variable if needed

3. check skew/kurtosis

jarque bera testing

• import scipy.stats as stats

• x = stats.jarque_bera(df[‘x’])

  • Ho: normally distributed

running OLS in python

x = df[[‘x1’, ‘x2’]]

y = df[‘y’]

x = sm.add_constant(x)

model = sm.OLS(x,y).fit()

print(model.summary())

unit root

a feature of non-stationary time series data

key library for ADF test

from statsmodels.tsa.stattools import adfuller

key library for KPSS test

from statsmodels.tsa.stattools import kpss

key conclusion of ADF and KPSS tests

• reject Ho in ADF + fail to reject Ho in KPSS = likely stationary

• fail to reject Ho in ADF + reject Ho in KPSS = likely not stationary

ADF test in python (all variable loop)

print(‘ADF Test Results’)

for column in df.columnsL

• print(‘\nColumn: ‘ + column)

• adftest = adfuller(df[column], autolag=’AIC’)

• print(‘ADF Stat: ‘ + str(adftest[0]))

• print(‘P-Value : ‘ + str(adftest[1]))

• if adftest[1] <= 0.05:

  • print(‘Reject Ho, the series is stationary)

• else:

  • print(Fail to reject Ho, the series isn’t stationary)

KPSS test in python (all variable loop)

print(‘KPSS Test Results’)

for column in df.columnsL

• print(‘\nColumn: ‘ + column)

• kpsstest = kpss(df[column], regression=’c’, nlags=’auto’)

• print(‘KPSS Stat: ‘ + str(kpsstest[0]))

• print(‘P-Value : ‘ + str(kpsstest[1]))

• if kpsstest[1] <= 0.05:

  • print(‘Reject Ho, the series isn’t stationary)

• else:

  • print(Fail to reject Ho, the series is stationary)