The residual is given by subtracting the actual value (in this case it's log returns) from the prediction value (generated by ). The following chart displays who we get the error term from the regression.
Then we do our calculation based on the residuals. The formula is basically sum of squared of the difference between error and it's 1 lagged term divided by sum of squared of all the error terms. It's a very simple test on residual sum of squares. The value you get is from 0 to 4.
When DW > 2, there's a possible negative autocorrelation.
When DW < 2, there's a possible positive autocorrelation.
Note: above 2 and below 2 is only possible autocorrelation, it might not be statistically significant.
If we want to know if the autocorrelation presence is significant or not. We need a Durbin Watson Stats Table. Based on the lookback period you use, you can find the critical value on the table (usually the first column).
Durbin Watson 0.05 Table
For the default setting 30 lookbacks, the 5% critical level for positive autocorrelation is 1.35. (We round to 1.4 on the default setting for convenience ). The other side for negative autocorrelation is just 4 - 1.35 = 2.65 due to its symmetry. For other lookbacks like 50, the critical value is 1.5 and 2.5, we just need to check the table to find the corresponding value. The user only has to find the lower threshold, the indicator will automatically give you the 4- lower threshold value on the other side.
As we have mentioned in the autocorrelation function and Hurst exponent . Positive autocorrelation means positive returns are more likely to be followed by positive returns and negative returns are more likely to be followed by negative returns. People may call it trending. Negative autocorrelation means positive returns are more likely to be followed by negative returns and negative returns may be followed by positive returns. People may call it mean-reverting.
The Durbin Watson test only tests the first-order autocorrelation. But there might also be significant autocorrelation in other lagged values. You can see the autocorrelation of other lags in our ACF.
We may also publish more advanced autocorrelation tests in the future.
Changed the color theme.
White means DW > 2, possible - autocorrelation / mean reversion
Orange means DW < 2, possible + autocorrelation / trending
Blue background means DW > upper critical value, Significant - autocorrelation / mean reversion
Red background means DW < lower critical value, Significant + autocorrelation / trending