Importing Data and Dropping Unnecessary Features
Go to Yahoo Finance and download data on the following three stock market indices for the longest possible time period: S&P500, DAX30, and Nikkei225. Import the data into MATLAB. Since your main variable of interest is the âadjusted closing priceâ of each index, you can drop all other variables.
After merging the data, you realize that all three time series start at different points in time. Choose the sample period so that it starts when you have for the first time observations for all three stock market indices available. The sample period ends on February 28th, 2020. If there is an observation missing (e.g., due to public holidays) for one time series, drop this observation for all three time series.
(a) For the sample period you have chosen, report the date of the first observation and the total number of observations for each time series in your solution paper. Plot the (adjusted closing) prices for all three time series, but do not put them in your solution paper. Based on these plots, do you think the three price time series are stationary?
Next, compute log returns for each stock market index and adjust your sample period accordingly. Again, plot the log returns for all three time series, but do not put them in your solution paper. Based on these plots, do you think the three return time series are stationary?
Finally, test all three log return time series for stationarity. Report the corresponding p-values. Based on a 5% significance level, what do you conclude from these results?
(b) You want to study the lead-lag relations between the log returns of the three stock market indices. A friend of yours suggests to start your analysis by running multivariate regressions. Comment on his suggestion.Â
(c) You decide to set up a two-dimensional VAR using the log returns of the S&P500 and the Nikkei225. Based on the Hannan-Quinn criterion, determine the optimal lag length for up to six lags. Estimate the model you identified as optimal. Report the parameter estimates, their t-statistics, and the adjusted R2
Next, focus on the first lag and on those parameter estimates that represent how one index affects the other one. Suppose at day t?1, there is a positive two-standard deviation shock to the log return of the S&P500 (or the log return of the Nikkei225, respectively). How would the log return of the Nikkei225 (or the log return of the S&P500, respectively) react at day t? Are your results economically significant?Â
(d) To take a closer look at the relation between the S&P500 and the Nikkei225, you decide to perform Granger causality tests on the log returns of both indices based on your results from exercise part (d). Write down the null and the alternative hypothesis (in terms of the actual parameter restrictions) of your tests and report the resulting p-values. Based on a significance level of 5%, what do you conclude from these results?
(e) Next, you decide to study the relation between the S&P500 and the Nikkei225 using impulse response functions based on your results from exercise part (d). Copy the plots that show how one stock market index responds to a shock in the other index in your solution paper. Comment on the economic significance of your results. (5 points)
(f) To study how much of the s-step-ahead forecast error variance of the Nikkeiâs log return is explained by innovations to the S&P500âs log return (and vice versa) for s = 1, . . . , 5 days, you perform a variance decomposition based on your results from exercise part (d).
Copy the plots that show how one stock market index responds to a shock in the other index in your solution paper. Comment on your results. (5 points)
(g) Finally, we want to study the lead-lag relation between the DAX30 and the S&P500 in a VAR(2). Repeat your analysis (from exercise parts (d), (e), (f), and (g)). Summarize your results briefly. What do you conclude from these results? (15 points)