(15 points) Dimension reduction and regularization You are a summer intern at Norges Bank Investment Management (NBIM). This is one of the world largest funds, and its main office is on Oslo. It is important for the company to predict future stock market developments. At your department you have access to daily return series from over 1000 international companies covering more than 2 decades. Your boss is interested in figuring out the co-movement in these returns series and how this co-movement might be related to developments in other markets, such as oil prices and interest rates. (a) (1.5 points) Mention at least two methods you can use to say something about the co-movement in the data. (b) (3 points) Explain Principal Component Analysis (PCA), and why a regression like f1,4 = BAoil Pricet + Ut can say something about how the return series relate to oil market develop- ments. (Here f1,t is the first factor estimate from PCA analysis using all the return series). How can you check how much variance is captured by each principal component? In what situations would this regression be a really bad idea. (c) (1.5 points) Explain two approaches you can use to interpret the results from Principal Com- ponent Analysis. (d) (3 points) Assume now that your boss wants to learn something about the linear relationship between the funds overall return and the return on the 1000 companies in your dataset. What is the dependent variable in this question, and what method would you use to estimate this relationship; OLS or LASSO? Explain your answer. (e) (3 points) In terms of LASSO, describe the role of the regularization parameter. What methods can you use to determine the optimal degree of shrinkage? (f) (3 point) What important transformations do you need to apply on your data prior to running PCA or LASSO? (15 points) Dimension reduction and regularization You are a summer intern at Norges Bank Investment Management (NBIM). This is one of the world largest funds, and its main office is on Oslo. It is important for the company to predict future stock market developments. At your department you have access to daily return series from over 1000 international companies covering more than 2 decades. Your boss is interested in figuring out the co-movement in these returns series and how this co-movement might be related to developments in other markets, such as oil prices and interest rates. (a) (1.5 points) Mention at least two methods you can use to say something about the co-movement in the data. (b) (3 points) Explain Principal Component Analysis (PCA), and why a regression like f1,4 = BAoil Pricet + Ut can say something about how the return series relate to oil market develop- ments. (Here f1,t is the first factor estimate from PCA analysis using all the return series). How can you check how much variance is captured by each principal component? In what situations would this regression be a really bad idea. (c) (1.5 points) Explain two approaches you can use to interpret the results from Principal Com- ponent Analysis. (d) (3 points) Assume now that your boss wants to learn something about the linear relationship between the funds overall return and the return on the 1000 companies in your dataset. What is the dependent variable in this question, and what method would you use to estimate this relationship; OLS or LASSO? Explain your answer. (e) (3 points) In terms of LASSO, describe the role of the regularization parameter. What methods can you use to determine the optimal degree of shrinkage? (f) (3 point) What important transformations do you need to apply on your data prior to running PCA or LASSO
