What is the 'Durbin Watson Statistic'

The Durbin Watson statistic is a number that tests for autocorrelation in the residuals from a statistical regression analysis. The Durbin-Watson statistic is always between 0 and 4. A value of 2 means that there is no autocorrelation in the sample. Values from 0 to less than 2 indicate positive autocorrelation and values from more than 2 to 4 indicate negative autocorrelation.

BREAKING DOWN 'Durbin Watson Statistic'

Autocorrelation can be a significant problem in analyzing historical data if one does not know to look out for it. For instance, since stock prices tend not to change too radically from one day to another, the prices from one day to the next could potentially be highly correlated, even though there is little useful information in this observation. In order to avoid autocorrelation issues, the easiest solution in finance is to simply convert a series of historical prices into a series of percentage-price changes from day to day.

Durbin Watson Statistic Calculation

The formula for the Durbin Watson statistic is rather complex, but involves the residuals from an ordinary least squares regression on a set of data. The following example illustrates how to calculate this statistic.

Assume the following (x,y) data points:

Pair one = (10, 1,100)

Pair two = (20, 1,200)

Pair three = (35, 985)

Pair four = (40, 750)

Pair five = (50, 1,215)

Pair six = (45, 1,000)

Using the methods of a least squares regression to find the "line of best fit", the equation for the best fit line of this data is:

Y = -2.6268x + 1,129.2

This first step in calculating the Durbin Watson statistic is to calculate the expected "y" values using the line of best fit equation. For this data set, the expected "y" values are:

Expected Y(1) = (-2.6268 x 10) + 1,129.2 = 1,102.9

Expected Y(2) = (-2.6268 x 20) + 1,129.2 = 1,076.7

Expected Y(3) = (-2.6268 x 35) + 1,129.2 = 1,037.3

Expected Y(4) = (-2.6268 x 40) + 1,129.2 = 1,024.1

Expected Y(5) = (-2.6268 x 50) + 1,129.2 = 997.9

Expected Y(6) = (-2.6268 x 45) + 1,129.2 = 1,011

Next, the differences of the actual "y" values versus the expected "y" values, the errors, are calculated:

Error(1) = (1,100 - 1,102.9) = -2.9

Error(2) = (1,200 - 1,076.7) = 123.3

Error(3) = (985 - 1,037.3) = -52.3

Error(4) = (750 - 1,024.1) = -274.1

Error(5) = (1,215 - 997.9) = 217.1

Error(6) = (1,000 - 1,011) = -11

Next these errors must be squared and summed:

Sum of errors squared = (-2.92 + 123.32 + -52.32 + -274.12 + 217.12 + -112) = 140,330.81

Next, the value of the error minus the previous error are calculated and squared:

Difference(1) = (123.3 - (-2.9)) = 126.2

Difference(2) = (-52.3 - 123.3) = -175.6

Difference(3) = (-274.1 - (-52.3)) = -221.9

Difference(4) = (217.1 - (-274.1)) = 491.3

Difference(5) = (-11 - 217.1) = -228.1

Sum of differences square = 389,406.71

Finally, the Durbin Watson statistic is the quotient of the squared values:

Durbin Watson = 389,406.71 / 140,330.81 = 2.77

A rule of thumb is that test statistic values in the range of 1.5 to 2.5 are relatively normal. Any value outside this range could be a cause for concern. The Durbin–Watson statistic, while displayed by many regression analysis programs, is not applicable in certain situations. For instance, when lagged dependent variables are included in the explanatory variables, then it is inappropriate to use this test.

  1. Residual Sum Of Squares - RSS

    A residual sum of squares is a statistical technique used to ...
  2. Error Term

    An error term is a variable in a statistical model, which is ...
  3. Least Squares Method

    The least squares method is a statistical technique to determine ...
  4. Regression

    A statistical measure that attempts to determine the strength ...
  5. Line Of Best Fit

    The line of best fit is an output of regression analysis that ...
  6. Nonlinear Regression

    Nonlinear regression is a form of regression analysis in which ...
Related Articles
  1. Tech

    Will IBM's Watson Group Turn Data Into Revenue?

    IBM made a major splash at CES with announcements regarding its data analytics ventures. Will it succeed?
  2. Tech

    IBM Makes Acquisition, Creates New Financial Services for Watson (IBM)

    IBM is planning to make its Watson's capabilities available to bankers to deal with increasingly complex regulation.
  3. Tech

    IBM Isn't Worried About Its Stock Tanking. This Is Why.

    IBM is experiencing a dearth of revenue growth and earnings performance as its older business channels die on the vine. The company is making a shift though to faster, growing segments and the ...
  4. Tech

    The Other Side of IBM's Watson A.I. Solution

    Manufacturing is often the first industry people think of when they consider where jobs could be lost as artificial intelligence systems grow in reach, though those concerns have yet to be borne ...
  5. Tech

    Square Surpasses $1B in Business Loans (SQ)

    Square reported Q3 software and data product revenue up 140% over last year, as Square Capital opens up and builds out with an array of new partnerships.
  6. Insights

    IBM's Watson Meets Salesforce's Einstein in New Partnership

    The two tech giants are clubbing IBM’s Watson and Salesforce’s Einstein to bolster sale of data-analytics and predictive offerings.
  7. Tech

    What is Square, Inc?

    Find out how Square helps small businesses accept credit cards, track sales and inventory through their mobile point of sale (POS) systems.
  8. Tech

    Square Inc. to Report Q3 Earnings (SQ)

    The global fintech leader may be positioned to secure its fourth consecutive earnings beat since its public debut in November of last year.
  9. Trading

    When Is A Bull Market Not A Bull Market?

    During some bull or bear moves in the stock markets, investors will be going with the trend, but day traders may find they cannot.
  10. Investing

    How to Pick the Best Stocks? Listen to Customers (AMZN, PZZA)

    Rated top in customer service, these companies have delivered impressive stock performance over the past year.
  1. In what types of economies are regressive taxes common?

    Understand the three main taxation systems, regressive, proportionate and progressive, and learn where regressive tax systems ... Read Answer >>
  2. How is residual value of an asset determined?

    Understand what the residual value of an asset is and how the residual value of an asset is calculated. Learn how residual ... Read Answer >>
  3. How do you calculate variance in Excel?

    To calculate statistical variance in Microsoft Excel, use the built-in Excel function VAR. Read Answer >>
  4. What is the difference between residual income and passive income?

    Learn how passive income helps pay the bills with little work involved. Determine how residual income affects your ability ... Read Answer >>
Trading Center