I am trying to find if the stock market movements on average and in extreme conditions do affect gold prices. I am following the regression model proposed by Baur and McDermott (2010) which is given as:
All models are estimated simultaneously with maximum likelihood methods as mentioned in their published paper which I don’t know how to apply it.
Below is what I have done:
reg <- read.csv(file = "MVreturnsqreg.csv")
The csv file contain time series of gold, S&P500 10 Quantile, S&P500 5 Quantile, S&P500 1 Quantile.
I have used the following regression command in R which I am not sure if it is the correct way to do and whether I can use OLS-regression with time series data. (if not, what is the right type of regression?)
goldregression= lm (reg$gold ~ reg$sp500 + reg$q10sp + reg$q5sp + reg$q1sp)
Below is the output of the regression model, but the estimates at all quantiles are not significant.
Also, I don't know how to take heteroskedasticity into consideration? I know GARCH (1,1) can take care of that, but how to estimate it with other models (1,2) at the same time? How can I Incorporate the above OLS-Regression to GARCH-model in order to receive fitted coefficients? or how to fit GARCH (1,1) model in the regression model? I don’t know which way it works.
If I use "rugarch" package to model GARCH(1,1), I would only get the parameters regarding the volatility equation ( mu, omega, alpha, beta) but not coefficients of my independent variables.
If I have to use GARCH method, where do I find the estimations for my independent variables after using the GARCH?