Regression / Time Series BP Stock Model

The date of the oil spill in the Gulf of Mexico was April 20, 2010.  British Petroleum stock has declined 54.6% from the close of 4/20/2010 to close 6/25/10 which is 48 trading days.  Volume has gone from 3.8 million on April 20th to 93 million on June 25th with a max of 240 million on June 9th. I am going to fit a simple regression and time series model to predict BP stock price based solely on price and volume. 

Below is an ANOVA table of a regression between change in price as a dependent variable and change in volume as an independent variable.  The negative sign for change in volume indicates as volume increases, BP stock has declined over this time period and is statistically significant.


The residuals are auto-correlated as this is a time series.  I am going to fit an AR(2) model to the residuals of the regression.  An AR(2) turned out to be the best fit after examining various ARIMA models and GARCH / ARCH models. 

To examine the fit of the model, an estimator of variance needs to be created using the actual stock prices and the fitted values.  Mean squared error or MSE is calculated below:

For this model, MSE = 2.8.

For only looking at price changes and volume, this is a fairly accurate fit and predictor although there are a few trouble points.  Accuracy could be increased by adding to the model.  

Disclaimer:  Please note this is a demonstration and for academic use only.