Exponential smoothing method is commonly used in output forecasting. Among all the forecasting methods, the simple full-period average method uses all the past data of time series equally. The moving average rule does not consider longer-term data, and gives more weight to recent data in the weighted moving average method; Exponential smoothing method combines the advantages of full-period average and moving average, and does not abandon the past data, but only gives the degree of influence that gradually weakens, that is, with the distance of data, gives the weight that gradually converges to zero. The exponential smoothing method will be introduced in detail below.

The basic formula of exponential smoothing method is:

St=ayt+( 1-a)St- 1

Where St-is the smooth value of time t;

Yt-the actual value of time t;

Actual value of St- 1- time T- 1;

A- smoothing constant, the value range is [0,1];

According to this formula:

1.St is the weighted arithmetic mean of yt and St- 1. With the change of a value, determine the influence degree of yt and St- 1 on St. When a takes 1, St = yt；; When a takes 0, St= St- 1.

2.St can be traced back to St-t+ 1, including all data. The smoothing constant decreases exponentially, so it is called exponential smoothing method. The value of exponential smoothing constant is very important. The smoothing constant determines the smoothing level and response speed to the difference between the predicted value and the actual result. The closer the smoothing constant a is to 1, the faster the long-term actual value drops to the current smoothing value. The closer the smoothing constant A is to 0, the slower the influence of the long-term actual value on the smoothing value of this period will decrease. Therefore, when the time series is relatively stable, you can choose a larger A; When the time series fluctuates greatly, a smaller value should be taken to avoid ignoring the influence of the long-term actual value. In the output forecast, the value of smoothing constant depends on the product itself and the manager's understanding of the connotation of good response rate.

3. Although St includes the influence of full-period data, only two values yt and St- 1 are needed in actual calculation, plus a constant A, which makes the exponential moving average have the property of recurrence period by period and brings great convenience to prediction.

4. According to the formula S1= ay1+(1-a) s0, when the exponential smoothing method is used to start collecting data, there is no y0. S0 can't be generated, so naturally, S 1 can't be obtained according to the exponential smoothing formula. Exponential smoothing method defines S 1 as the initial value. The same is true for the determination of initial value.

If the historical data before y 1 can be found, the determination of the initial value S 1 is not a problem. When there are a lot of data, the least square method can be used, but the exponential smoothing method itself can not be used to determine the initial value, because the data will be exhausted.

If there are only data starting from y 1, then the methods to determine the initial value are: 1) take S 1 equal to y1; 2) After accumulating some data, take S 1 as the simple arithmetic average of the previous data, such as: S 1=(y 1+ y2+y3)/3 and so on.