Investigating stylized facts of asset returns

Stylized facts are statistical properties that are present in many empirical asset returns (across time and markets). It is important to be aware of them because when we are building models that are supposed to represent asset price dynamics, the models should be able to capture/replicate these properties.

In this recipe, we investigate the five stylized facts using an example of daily S&P 500 returns from the years 2000 to 2020.

Getting ready

As this is a longer recipe with further subsections, we import the required libraries and prepare the data in this section:

1. Import the required libraries:

   import pandas as pd
   import numpy as np
   import yfinance as yf
   import seaborn as sns
   import scipy.stats as scs
   import statsmodels.api as sm
   import statsmodels.tsa.api as smt
   

2. Download the S&P 500 data and calculate the returns:

   df = yf.download("^GSPC", 
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