What about the exponential smoothing index?

One 、 application

Exponential smoothing can be further split into one pass smoothing , Quadratic smoothing and cubic smoothing （ namely Holt-Winters Law ）, The one-time smoothing method is the weighted prediction of historical data , The quadratic smoothing method is suitable for data with certain linear trend , The cubic smoothing method smoothes again on the basis of the quadratic smoothing method , It is suitable for use when there is a certain curve trend relationship , Generally, the cubic smoothing method is used more .

Whatever the smoothing method , They all involve initial values S0 Coefficient of smoothness alpha Two parameter values in total , The initial value is the initial starting point of smoothing , Generally, before fetching data 1 period ,2 period ,3 period ,4 Period or 5 The average value of the period is taken as the initial value , If there are fewer data sequences, the initial value S0 More averages from previous periods should be taken , Because the importance of early stage is relatively high when there are few data sequences . in the light of alpha Value parameter , The awareness lies in the weight of new data ,alpha The larger the value, the higher the weight of the new data and the lower the weight of the original forecast value ,alpha=0 It means that the forecast value of the next period is completely equal to the forecast value of the current period ;alpha=1 It means that the forecast value of the next period is equal to the forecast value of the current period . If the data fluctuates little , commonly alpha Take a smaller value, for example 0.1~0.5 Between , If the data fluctuates greatly and alpha The value is relatively large , such as 0.6~0.8 Between .

Two 、 operation

SPSSAU operation

（1） Click on SPSSAU Comprehensive evaluation ‘ Exponential smoothing ’ Button . Here's the picture

SPSSAU The dashboard

（2） Drag and drop the data and click start analysis

3、 ... and 、 Analysis steps

 

Four 、 Case background

There is a province at present 1978~1988 Data on investment in fixed assets owned by the whole people in , total 11 Annual data , The data are shown in the table below , Now I hope to predict 1989 and 1990 Data of total fixed asset investment in ：

5、 ... and 、 The results of the analysis

SPSSAU The resulting analysis results are as follows

1. Parameter settings

The table above shows the default settings ,3 The values of the parameters all let SPSSAU Automatically . Final SPSSAU The cubic smoothing method is automatically selected as the optimal model , And the initial value is automatically set to 20.05,alpha The value is automatically selected as 0.4, Based on this automatic selection , Root mean square error of the final model RMSE by 18.8, The following table

2. Root mean square error value RMSE

Because this case 3 Parameter values include smoothing type , Initial value S0 and alpha value , All let SPSSAU Automatic selection ,SPSSAU Automatically set the initial value to 20.05, And traverse on this basis 3 Cases and 11 Kind of alpha Total values 33 Two combinations , Output 33 Corresponding to each combination RMSE value , Find out when the initial value is 20.05, And alpha The value is 0.4 And the model result obtained by cubic smoothing is the best . The optimal combination is marked in blue in the above table . The model prediction results are shown in the table below

3. Model predictive value table

Calculation formula

One time exponential smoothing

In style    by t Actual observations for the period ,  by t The forecast value of the period ,  Is the smoothing coefficient （0< <1）

Phase II forecast value

Forecast value of the third period

t Period forecast

As can be seen from the above table ： backward 1 Period namely 1989 The fixed asset investment in is predicted to be 270.8 Billion , And 1990 The fixed asset investment in is predicted to be 321.526. The fitting diagram of prediction effect is as follows .

PS： On three smoothing methods , Initial value S0 and alpha The values are described in the following table