Time Series Forecasting as a Measure

The Combined Forecasting

Actual complex time series forecasting is a difficult problem. Complex combined forecasting method, which is proposed by J. M. Bates and C. W. J. Granger in 1969, is the actual time series forecasting a new stage of development. The linear combined forecasting can be expressed as shown below.

For the time series, t = 1, 2, …,N methods using the predicted results:

Here, is the i-th test phase forecasting method T a predictive value. is residual, that mean value is 0., The correlation of any two residuals between and coefficient , i, j=1, 2, …, N, i≠ j.

In general, we do not assume that is normally distributed. obey arbitrary distribution. It because that we are difficult to determine the specific distribution pattern of the noise an forecasting error. Thought assumed to follow a normal distribution is reasonable, when the T is larger.

The results of the linear combined forecasting is:

The optimal weights of linear combined forecasting became find , that of the, t=1,2, …, T (3) is in the minimum variance.

is the residual of a forecasting result. Its mean may not 0, when the linear combined forecasting is biased. In this case, we can analyze the historical data to estimate the residual mean of , and then to be corrected. The variance of the residual generally consists of two parts. One part is the noise in the historical data, which can’t been forecasted. Another part comes from the forecasting of the defect. Any kind of forecasting method has its own shortcomings, a single method to predict will cause additional errors. The combined forecasting is powerless for the first part factor, and it forms predicted limits. We can improve the forecasting methods and use of combined forecasting, which can significantly reduce the forecasting error.

Impact Factors Of The Combined Forecasting

The main factors affecting combined forecasting accuracy rate is: