A Stock Market Model

(Adapted from Mooney and Swift, A Course In Mathematical Modeling.)

Background

Conventional wisdom says that over the long term, the stock market grows exponentially. The short-term ups and downs are essentially noise. This project explores this idea. One problem is trying to measure the stock market. We will use one common measurement instrument, the Dow Jones Industrial Average (the Dow). (other measures?)

Data

Find monthly (at least) data for the Dow for the last 30 years. You can find this data either in the library or online. One source is Yahoo! Finance: the ticker symbol for the Dow is ^DJI.

Questions

1. Plot the data you have found, and the log plot of the data. Using the log plot, find the best-fitting exponential model. How well does this model fit the data? Your comments should include both a visual inspection of the model and the original data, and a discussion of R².

2. If you invested $1,000 today and the Dow continued to behave as it had in the past, use your exponential model to predict how much your investment would be worth in 30 years.