QM

The main objective of the Durbin-Watson test is to determine first-order autocorrelation among the residuals. This means it looks at the deviation from yesterday’s residual and looks for patterns. The resulting value d can take on values between 0 and 4.

A value of 2 implies no autocorrelation whatsoever. A significantly larger value indicates negative autocorrelation and a value close to zero implies strong positive autocorrelation.

There are some major differences between the Lagrange and the Kuhn-Tucker approach, even though both represent a saddle function. The largest of them being the inequalities in the Kuhn-Tucker restrictions. It is important that all the restrictions have to use a ≤ in order to define the set of feasible decisions.

Another difference is, that the multipliers are non-negative. In the world of Lagrange, they can only be negative, but for Kuhn-Tucker, it would not make sense.

This leads to the Complementary Condition: Either the multiplier or the restriction have to be equal to zero. If the multiplier is zero, the restriction is not binding and the optimal solution is not on its border. Therefore, the derivative on the border of the restriction is not zero. If the multiplier is positive, the restriction has actual value of the decision maker. Hence, the optimum is located on the border of said restriction.

--> Kuhn-Tucker only works for maximization problems. If there is a minimization problem, you need to switch signs and multiply by (-1).