Engle, Ito and Lin (1990) (https://www.jstor.org/stable/2938189) explain volatility clustering in exchange rates and formulate meteor shower and heat wave hypotheses. The heat wave hypothesis is that the volatility has only country-specific autocorrelation. Alternatively, the meteor shower is a phenomenon of intra-daily volatility spillovers from one market to the next.

a Formally introduce and explain GARCH models associated with meteor shower and heat wave hypotheses. Which coefficients can be tested to verify each of these hypotheses?

b Table 2 in Engle, Ito and Lin (1990) provides result for testing meteor showers and heat waves in the Pacific region, Tokyo, Europe and the United States. Ignore the results for the Pacific region and provide a similar Table using more recent data for the bond market from log returns 9 series.wf1. Can you broadly confirm that the volatility patterns in the bond market are similar to the foreign exchange market?

c Estimate News Impact Curves (NICs) for Japan, Europe and US and plot them. Explain how different they are. Do you observe any issues with these NICs?

d A relationship between the risk and expected return of an asset depends upon attitudes toward risk of asset holders. Which volatility model would you choose to capture this relationship?