Significance testing of model parameters

GARCH Models in Python

Chelsea Yang

Data Science Instructor

Do I need this parameter?

  • Is it relevant

  • KISS: keep it simple stupid

  • Always prefer a parsimonious model
GARCH Models in Python

Hypothesis test

  • Null hypothesis (H0): a claim to be verified

  • H0: parameter value = 0

  • If H0 cannot be rejected, leave out the parameter

GARCH Models in Python

Statistical significance

  • Quantify having the observed results by chance
  • Common threshold: 5%
GARCH Models in Python

P-value

  • The odds of the observed results could have happened by chance

  • The lower the p-value, the more ridiculous the null hypothesis looks

  • Reject the null hypothesis if p-value < significance level

GARCH Models in Python

P-value example

print(gm_result.summary())

P-value in summary

print(gm_result.pvalues)

mu           9.031206e-08
omega        1.619415e-05
alpha[1]     4.283526e-10
beta[1]     1.302531e-183
Name: pvalues, dtype: float64
GARCH Models in Python

T-statistic

  • T-statistic = estimated parameter / standard error
  • The absolute value of the t-statistic is a distance measure
  • If |t-statistic| > 2: keep the parameter in the GARCH model
GARCH Models in Python

T-statistic example

print(gm_result.summary())

T-statistics in summary

print(gm_result.tvalues)

mu           5.345210
omega        4.311785
alpha[1]     6.243330
beta[1]     28.896991
Name: tvalues, dtype: float64

# Manual calculation
t = gm_result.params/gm_result.std_err
GARCH Models in Python

Let's practice!

GARCH Models in Python

Preparing Video For Download...