Question 3 [Financial price data]

(a) Download price data for a financial asset of your choice. [Hint: possibilities here include stock price data from yahoo finance or cryptocurrency data from coinmarketcap.com]. Explain why the asset or index you have chosen is interesting and give the precise dates for which you have collected the data.

(b) Download the data into R and calculate the log-returns. List the R commands used.

(c) Fit an ARCH(1) model to the log-returns in part (b) and test for the presence of an ARCH effect within this data. List the R commands and R packages used.

(c) Fit a GARCH (1, 1) model to the log-returns in part (b) and test for the presence of ARCH and GARCH effects within this data. List the R commands and R packages used.

(e) List the stylised empirical facts of financial time series.

(f) [Independent research required]. Explain how more advanced family GARCH models can be fitted to the data in part (b) using R.