Table 6 Comparison of results using the Diebold and Yilmaz (2012) Model and the Baruník and Křehlík (2018) Model

Total volatility spillover indicator, it is observed that, on average, within the entirety of our sample equals 54%

The highest volatility spillover transmitter is Microsoft, with a value of 81.9% to others, followed by Chevron, which has a value of 67.4% to others

Tether (USDT) has a weight of 14.4%, which is the lowest transmutation for the other

Chevron is the highest receiving with a value of 66.1%, and Tether is the lowest receiving with volatility spillovers of 27.0%

The magnitude of the dynamics spillovers surpassed the threshold of 50% in the middle of 2019 and reached 85%. Significantly, during the COVID-19 pandemic

The period characterized by the most pronounced directional volatility spillovers from – to companies was observed during the COVID-19 pandemic in the year 2020 and the volatility spillovers rise about 40% for each

Then the volatility spillovers witnessed resurgence in 2022 because of the Russia–Ukraine crisis and the resulting food crisis and price inflation

Bitcoin, Ethereum, Chevron, ConocoPhilips, Apple and Microsoft are net sender, while other is net receiver

Baruník and Křehlík (2018) approach shows time–frequency spillovers with different terms (short, medium, and long)

The total volatility spillovers for the short-term period (from 1 to 4 days) are 47.81%, while in the medium term (from 4 to 10 days) they are 41.82%, and in the long-term (from 10 days) they are 45.17%

The highest value for volatility spillovers occurs in the short-term horizon

The effects of volatility spillover transmission from one market to others are of brief duration

Chevron contributed the most to short and medium-term volatility spillovers by 7.16% and 7.41%, respectively

Exxon contributed the most to long-term volatility spillovers by 5.01%

Exxon had the second highest contribution in the short term, followed by Microsoft (5.51%), ConocoPhillips (4.42%), Alphabet (4.36%) and Bitcoin (4.03%), so they were the highest transmitter of volatility to the others

Energy companies have the most contribution volatility spillovers in our sample

In the long term, Exxon, Microsoft, ConocoPhillips, and Bitcoin were the highest transmitter of volatility to the others, while USDT was the highest receiver from the others