Variability in Times of Disease. Application of ARMA-GARCH in Modelling and Predicting Volatility of S&P500 Index Return Rates in COVID-19

Aim: The article considers the time series case of the closing prices of the S&P500 index over the period from January 2020 to April 2021. The author selected the best ARMA(p,q)-GARCH(1,1) models with different forms of probability density functions. The errors of the forecasts generated both in terms of logarithmic returns and their variability were compared. Methodology: The study followed the Box-Jenkins procedure. Applying the information criterion the study considered the best among these models with normal, skewed Student’s t, generalised error and generalised hyperbolic distribution. Results: The author obtained the following representations: ARMA(2,0)-GARCH(1,1) and ARMA(0,2)-GARCH(1,1), with normal, skewed Student’s t and generalised error distribution. The assessment of forecast accuracy showed that in the case of conditional variance forecasts, the ARMA(2,0)GARCH(1,1) models with a normal distribution and a generalised error distribution were the best. The largest errors of conditional variance forecasts were generated by models with a skewed Student’s t-distribution. Implications and recommendations: It is worth extended the study to models based on the range of fluctuations (such as Range GARCH-RGARCH or Conditional Autoregressive Range Model-CARR). Originality/value: The author considered models with various probability density functions, showing that such diversity was important when looking for the best models in times of high volatility.