to.) Consider the 8&P500 index from January 1, 1990 to June 30. 2019. The data is available using quantmod. and the symbol for the index is \"GSPC. Fit an ARMA model to the index return time series (calculate the returns using the adjusted closing prices), and a GARCH model for the index volatility. id.) Calculate the correlation between the VIX and the squared returns of the S&P500 index, and the tted volatility using the GARCH model. Calculate the correlation over the entire time sample. Calculate the correlation on a year by year basis and plot the annual correlation. is.) Considering the correlation values, is the 'v'lX a good representative of the volatility of the index? If not. why? Propose a way to test this in a quantitative way