A Bootstrap Analysis of the Nikkei 225

This study intends to find out whether or not the Nikkei 225 evolves over time in accordance with the following four widely used processes for determining stock prices: random walk with a drift, AR(1), GARCH(1,1), and GARCH(1,1)-M. Given the fact that, in actuality, we have but one sample of time series data, the motivation of this study is to make use of the bootstrap technology to deal with this one-sample problem. Specifically, we use the bootstrap technique to generate 2,000 artificial Nikkei series from each process and compute the return from the trading rule for each of the 2,000 artificial Nikkei series. Then, we construct a 95% bootstrap percentile interval with these 2,000 returns and determine if it contains the return computed from the actual Nikkei series. If it does, we claim that returns from the artificial Nikkei series are in agreement with those from the actual Nikkei series. Our results show that, of the four processes, GARCH(1,1)-M generates returns that are most agreeable with those computed from the actual Nikkei series. An important implication of this study is that a proper model for pricing Nikkei-related derivatives is one that uses the GARCH(1,1)-M process to depict the dynamics of the Nikkei return series.