Determination of the Order of An AR(p) Model by Using Local Residual Sum of Squares

According to the demand in practice, the method of determining the order in an AR(p) model is extended, and the method of determining the order based on local residual sum of squares is introduced. This method shows that the theory of multiple objective programming and the local character of some sequences can be combined. An example shows that with the method of determining the order based on local residual sum of squares in AR(p), the precision of forecast values increases. The supremum of the order of the AR(p) model is given and proved.