Suppose I am conducting a research paper on time series data entitled “The Nexus Among Oil Price, Stock Market, and Exchange Rate During Recent Pandemic & Russia-Ukraine Crisis: Fresh Evidence from UK Economy”. Here I have taken three variables Stock Index (SI), Brent Oil Price (OP), and Exchange Rate (ER). I have taken time series data from 2014-2023 segmenting into four periods. 2014-2019 for Pre-covid Period; 2020-2021 for Covid Period; 2022-2023 for War Period and 2014-2023 for the Overall Period. My Research Questions are:
1. Does each variable have a direct influence on others?
2. Does each variable granger cause one another and does the stock market work as a mediating variable for shock transmission?
3. Is there any moderating impact of oil price on the dynamic conditional correlation (DCC) between the stock market and exchange rate?

For data analysis, I have checked other relevant literature.

For research question 1, most of them used the VAR model to check the direct influence of variables on each other. For research question 2, most of them used VAR Granger Causality and determined if the stock market transmits the shock as a mediating variable or not. I haven’t found any paper on my 3rd research question but a paper suggested a technique to address it in their future research question. I am giving their exact quotation, “The moderating effect of oil can be estimated by using the NARDL framework for studying the direct influence of OP on the DCCs between SI and ER”.

But the problem is that, for my 1st and 2nd, I can’t use the VAR model as I have autocorrelation and heteroskedasticity which I can’t remove even after log transforming or log differencing the variable. I also can’t use VECM Model either as my variables are not co-integrated from the Johansen co-integration test. Therefore give me a solution for my model. Which other econometric model can I use that takes autocorrelation and heteroskedasticity into account for my 1st and 2nd research questions as well as also give me guidelines on how to approach the analysis of my 3rd research question? I am really lost here. I don’t know how to analyze the process in R. And What about VAR-DCC-GARCH, I have seen some research paper used it. Does it suit my research question? If suited, include the R commands for VAR-DCC-GARCH too?