Problem 4.12 This problem is a sequel to Problem 4.11. It uses the data contained in the matrices SMORN.mat and SAFT.mat. Open and run the (data) script file spindicators.asc to create these two matrices. They contain the six indicators computed for the September S&P 500 futures contract from the mornings and afternoons transactions of the period ranging from June 1, 1998 to September 5, 1998.

1. Use the regression function computed for the kernel regression of the afternoon volatility ratio of the modified June contract data (fourth column of SAFT.mat) against the morning volatility ratio and rate of arrival indicators of the same modified June contract data

(fourth and fifth columns of SMORN.mat) to predict the afternoon volatility ratios given in the fourth column of SAFT.mat from the morning volatility ratio and rate of arrival indicators of SMORN.mat. Compute the sum of square errors.
In other words, use the June contract data as training sample and the September contract data as testing sample.
2. Redo the same thing using as explanatory variables the first two (linear combinations)
principal components of the six indicators found in the PCA analysis of the June matrix data done in Problem 4.11. Comment.