The accumulating method based on non-equidistant sequence and its applications

The accumulating method based on the non-equidistant sequence is proposed. Accumulated sum of each order of the non-equidistant sequence is given. Then the accumulating method can be applied to estimate parameters of the model built on the non-equidistant sequence. A new formula of the parameter estimation is proposed after introducing this method into the non-equidistant GM(1,1) model. Furthermore, a new forecasting formula is given, which is deduced directly from the defining pose of the model and can take the place of the white response. The analyzing results conclude that good effects are obtained when the accumulating method is applied into the non-equidistant GM(1,1) model and a good forecasting precision of the improved model is achieved.