## Blog #2 (08/14/17)

Hello everybody! In the past month, Dr. Parisi and I have made tremendous progress and it is quite upsetting that the summer is coming to such a close end! Our end goal at the moment is to submit a research paper for publication and we are currently at nine pages of analysis, figures, and information. We studied the behavior of extreme changes in stock market indices using extreme value methods.  Working with daily log returns we fit a generalized extreme value distribution to each return series, using various blocks (daily, monthly, yearly) to find the return level for various windows. Using the daily closing prices going back to the Great Depression for the DJIA and the S&P 500 as well as the closing prices for the Nikkei 225 and FTSE, we were able to utilize the different time ranges for each index which allowed us to compute these return level analyses. Throughout this whole project, we have used R to analyze the data as there are Extreme Value Theory (EVT) packages (fExtremes and evir). After calculating the returns, we found that for the S&P 500, the 20-period return level for monthly maxima is estimated at a 4.7% decline, and an estimated 11.7% decline for annual maxima. Over a 10-month/year return level, we can expect to see an estimated 3.6% decline for monthly maxima and an estimated 8% decline for annual maxima. For the Nikkei 225, we can expect an estimated 5.5% decline for monthly maxima and an estimated 11% decline annual maxima for the respective 20-period return levels. Ten-period return levels are 4.5% and 9% decline for monthly and annual maxima, respectively. For the DJIA, we can expect a 4.2% decline for monthly maxima and a 9% decline for annual maxima for the 20-period return level. The 10-period return levels are 3% decline (monthly) and 6.8% (annual). For the FTSE, the 20-period return levels are 3.9% decline for monthly maxima and an estimated 7% decline for annual maxima. The 10-period return levels are  3% and 5%, monthly and annual maxima, respectively. One of our final steps included using the parameters we found from the fitted distribution to simulate 100,000 values so that we can look at the number of exceedances to see the probability of having a market decline of 30%. When completed, I will attach our finalized research paper that we will submit for publication to this blog post. One of the challenges I came across for this research opportunity was learning to use R, a language that I had never used before this summer. With Dr. Parisi’s guidance and sample code, I am confident when I say that I have gained the basic knowledge needed to work with R but at the same time, there were bumps in the road when I couldn’t figure something out. This summer research project has taught me many things: R programming, stock market indices, return levels, market declines, how to fit a generalized extreme value distribution, and so much more. It was amazing to be working alongside an extremely knowledgable professor who has had previous experience working with the S&P 500. Working on this project over the summer makes me feel even more confident with my decision to major in Information Systems and I also wanted to thank Pace University for this amazing opportunity.

## Blog #1 (07/17/17)

Hello everybody! My name is Ezana Ceman and this is my first blog regarding my summer undergraduate research project with Dr. Parisi. The title of our project is “Estimating Return Periods for Extreme Value Shocks” and we have made really good progress so far. Dr. Parisi was my professor during my first semester of freshman year for CS 113, Mathematical Structures for Computer Science. He was an amazing professor and I enjoyed his class so much! I was so excited when he asked me if I would like to work on a summer research project with him. At first, I was given materials to review regarding how to program using R and what extreme value returns actually are. A majority of our research is being done using R since R is used for statistical modeling so this programming platform is perfect for our work. As of today, Dr. Parisi and I both collectively found the daily, monthly, and annual returns for the four stock market indices we are using; the S&P 500, the Nikkei 225, the FTSE 100, and the Dow Jones Industrial Average. We also found all of the parameters revolving the generalized extreme values (GEV) for all of the stock market indices as well. Dr. Parisi is going to look into all of our data gathered so far to see if there is any seasonality to see if there are any relations there for where the returns spike up or down. Seasonality is a characteristic where you can see if there is any predictability in seeing changes that occur on a yearly basis in a time series. Before our next meeting, I will be gathering data that goes back to the Great Depression as our current data ranges from 1985-May 2017 for the DJIA, 1950-May 2017 for the SPX, 1984-May 2017 for the NIK, and 2009-May 2017 for the FTSE. Having data that goes even further the stock market indices that were around back in the 1920s and 30s will help us have stronger and more concrete return values that will overall help us reach a more valid conclusion. I am looking forward to coming up with a paper for publication with Dr. Parisi and hopefully we find some cool and new interesting commonalities between all of the years and return values so that we can share something new with the world! I attached a few screenshots of some of the plots we have created to go along with our data just to have some visuals within this post and these were all created using R programming!