What Is the Durbin Watson Statistic?
Let me explain the Durbin Watson statistic directly: it's a test you use to check for autocorrelation in the residuals from a statistical model or regression analysis. This statistic always falls between 0 and 4. If you get a value of 2.0, that means no autocorrelation is detected in your sample. Values from 0 to less than 2 signal positive autocorrelation, and from 2 to 4 indicate negative autocorrelation.
Think about a stock price with positive autocorrelation—it means yesterday's price positively correlates with today's, so if it dropped yesterday, it's likely to drop today too. On the flip side, negative autocorrelation means a drop yesterday increases the chance of a rise today.
Key Takeaways
- The Durbin Watson statistic tests for autocorrelation in a regression model's output.
- It ranges from zero to four, with 2.0 meaning zero autocorrelation.
- Values below 2.0 show positive autocorrelation, and above 2.0 indicate negative autocorrelation.
- Autocorrelation is handy in technical analysis, focusing on price trends via charts rather than a company's fundamentals.
Understanding the Durbin Watson Statistic
Autocorrelation, or serial correlation, can mess up your analysis of historical data if you're not watching for it. For example, stock prices don't swing wildly day to day, so prices from one day might correlate strongly with the next, but that correlation might not tell you anything useful. In finance, you can dodge this by converting historical prices into daily percentage changes.
That said, autocorrelation has its place in technical analysis, where you're all about price trends and relationships through charting, ignoring things like financial health or management. As a technical analyst, you can use it to gauge how past prices influence future ones.
It can reveal if there's momentum in a stock. Say a stock has high positive autocorrelation and has been gaining for days—you might expect that trend to continue upward in the coming days.
Fast Fact
The Durbin Watson statistic is named after statisticians James Durbin and Geoffrey Watson.
Special Considerations
Here's a rule of thumb: DW values between 1.5 and 2.5 are usually fine. Anything outside that range might be a red flag. Many regression programs spit out this statistic, but it's not always applicable. For instance, if your model includes lagged dependent variables as explanatory variables, skip this test—it's not appropriate.
Example of the Durbin Watson Statistic
The formula for the Durbin Watson statistic is complex, but it boils down to residuals from an ordinary least squares (OLS) regression. I'll walk you through an example with these (x, y) data points: Pair One (10, 1100), Pair Two (20, 1200), Pair Three (35, 985), Pair Four (40, 750), Pair Five (50, 1215), Pair Six (45, 1000).
First, find the line of best fit using least squares: Y = -2.6268x + 1129.2.
Now, calculate expected Y values: For x=10, 1102.9; x=20, 1076.7; x=35, 1037.3; x=40, 1024.1; x=50, 997.9; x=45, 1011.
Next, find the errors (actual Y minus expected Y): -2.9, 123.3, -52.3, -274.1, 217.1, -11.
Square and sum these errors: 140,330.81.
Then, calculate differences between consecutive errors: 126.2, -175.6, -221.9, 491.3, -228.1. Square and sum them: 389,406.71.
Finally, the DW statistic is 389,406.71 / 140,330.81 = 2.77. Note that rounding might affect the tenths place.
