## Description

## Problem Description.

1. The attached file DJI 2009.csv is downloaded from finance.yahoo.com. It contains the

historical prices of the Dow Jones Industrial Average (ˆDJI) from October 1, 1928 to

February 20, 2009. plot the time series of the adjusted closing prices.

The data set is saved as a .csv file. You can read it into Matlab using function load. Try

‘help load’ in Matlab for more details. Below is a command line that I’ve used:

load(’DJI_2009.csv’, ’-regexp’, ’^Date|^Open|^High|^Low|^Close|^Volume|^Adj Close’);

2. Take the value for the last 300 days. Fit a smoothing spline to these data points. First

choose different values of the algorithmic parameter to fit the splines. Secondly, use the

generalized cross validation criterion to determine the value of the algorithmic parameter.

Compare the results for the different values of the algorithmic parameter. Explain what

you observe.

3. Note that for the values of 300 days, you may still use the codes that are provided in the

lecture notes. If you would like to fit a penalized smoothing spline for the last 3000 days,

if the same codes are used, it would take a long time to run. In theory, the computational

complexity is O(n): an efficient implementation can significantly reduce the running time.

Write a more efficient implementation.

0 50 100 150 200 250 300 350

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

x 104 Noisy Observations

x

y

Noisy Observations

Fitted Spline