Durbin Watson Statistic

What Is the Durbin Watson Statistic?

The Durbin Watson (DW) statistic is a test for autocorrelation in the residuals from a statistical model or regression analysis. The Durbin-Watson statistic will continuously have a value going somewhere in the range of 0 and 4. A value of 2.0 shows there is no autocorrelation recognized in the sample. Values from 0 to under 2 point to positive autocorrelation and values from 2 to 4 means negative autocorrelation.

A stock price showing positive autocorrelation would demonstrate that the price yesterday has a positive correlation on the price today — so assuming that the stock fell yesterday, all things considered, it falls today. A security that has a negative autocorrelation, then again, impacts itself after some time — so that assuming that it fell yesterday, there is a greater probability it will rise today.

The Basics of the Durbin Watson Statistic

Autocorrelation, otherwise called serial correlation, can be a huge problem in examining historical data in the event that one doesn't be aware to pay special attention to it. For example, since stock prices tend not to change too fundamentally over time one day to another, the prices over time might actually be highly connected, even however there is minimal valuable data in this perception. To stay away from autocorrelation issues, the least demanding solution in finance is to just change over a series of historical prices into a series of rate price changes from one day to another.

Autocorrelation can be valuable for technical analysis, which is generally concerned with the trends of, and connections between, security prices involving charting strategies in lieu of an organization's financial wellbeing or management. Technical analysts can utilize autocorrelation to perceive the amount of an impact past prices for a security have on its future price.

Autocorrelation can show in the event that there is a momentum factor associated with a stock. For instance, assuming that you realize that a stock historically has a high positive autocorrelation value and you saw the stock making strong gains throughout recent days, then you could sensibly anticipate the developments over the impending several days (the leading time series) to match those of the lagging time series and to move up.

The Durbin Watson statistic is named after statisticians James Durbin and Geoffrey Watson.

Special Considerations

A rule of thumb is that DW test statistic values in the scope of 1.5 to 2.5 are somewhat normal. Values outside this reach could, nonetheless, be a reason to worry. The Durbin-Watson statistic, while showed by numerous regression analysis programs, isn't applicable in certain circumstances.

For example, when lagged dependent factors are remembered for the illustrative factors, then, at that point, utilizing this test is improper.

Illustration of the Durbin Watson Statistic

The formula for the Durbin Watson statistic is somewhat complex yet includes the residuals from an ordinary least squares (OLS) regression on a set of data. The accompanying model outlines how to ascertain this statistic.

Expect to be the accompanying (x,y) data points:
$\begin &\text=\left( {10}, {1,100} \right )\ &\text=\left( {20}, {1,200} \right )\ &\text=\left( {35}, {985} \right )\ &\text=\left( {40}, {750} \right )\ &\text=\left( {50}, {1,215} \right )\ &\text=\left( {45}, {1,000} \right )\ \end$
Utilizing the methods of a least squares regression to view as the "line of best fit," the equation for the best fit line of this data is:
$Y={-2.6268}x+{1,129.2}$
This initial phase in working out the Durbin Watson statistic is to ascertain the expected "y" values utilizing the line of best fit equation. For this data set, the expected "y" values are:
$\begin &\textY\left({1}\right)=\left( -{2.6268}\times{10} \right )+{1,129.2}={1,102.9}\ &\textY\left({2}\right)=\left( -{2.6268}\times{20} \right )+{1,129.2}={1,076.7}\ &\textY\left({3}\right)=\left( -{2.6268}\times{35} \right )+{1,129.2}={1,037.3}\ &\textY\left({4}\right)=\left( -{2.6268}\times{40} \right )+{1,129.2}={1,024.1}\ &\textY\left({5}\right)=\left( -{2.6268}\times{50} \right )+{1,129.2}={997.9}\ &\textY\left({6}\right)=\left( -{2.6268}\times{45} \right )+{1,129.2}={1,011}\ \end$
Next, the differences of the real "y" values versus the expected "y" values, the errors, are calculated:
$\begin &\text\left({1}\right)=\left( {1,100}-{1,102.9} \right )={-2.9}\ &\text\left({2}\right)=\left( {1,200}-{1,076.7} \right )={123.3}\ &\text\left({3}\right)=\left( {985}-{1,037.3} \right )={-52.3}\ &\text\left({4}\right)=\left( {750}-{1,024.1} \right )={-274.1}\ &\text\left({5}\right)=\left( {1,215}-{997.9} \right )={217.1}\ &\text\left({6}\right)=\left( {1,000}-{1,011} \right )={-11}\ \end$
Next these errors must be [squared and summed](/amount of-squares):
$\begin &\text{Sum of Errors Squared =}\ &\left({-2.9}$
Next, the value of the mistake minus the previous blunder are calculated and squared:
$\begin &\text\left({1}\right)=\left( {123.3}-\left({-2.9}\right) \right )={126.2}\ &\text\left({2}\right)=\left( {-52.3}-{123.3} \right )={-175.6}\ &\text\left({3}\right)=\left( {-274.1}-\left({-52.3}\right) \right )={-221.9}\ &\text\left({4}\right)=\left( {217.1}-\left({-274.1}\right) \right )={491.3}\ &\text\left({5}\right)=\left( {-11}-{217.1} \right )={-228.1}\ &\text={389,406.71}\ \end$
At long last, the Durbin Watson statistic is the quotient of the squared values:
$\text={389,406.71}/{140,330.81}={2.77}$
Note: Tenths place might be off due to rounding errors in the figuring out

Highlights

The DW statistic goes from zero to four, with a value of 2.0 demonstrating zero autocorrelation.
Values below 2.0 mean there is positive autocorrelation or more 2.0 demonstrates negative autocorrelation.
The Durbin Watson statistic is a test for autocorrelation in a regression model's output.
Autocorrelation can be helpful in technical analysis, which is generally concerned with the trends of security prices involving charting methods in lieu of an organization's financial wellbeing or management.