This paper introduces the simple operation of realizing linear quadratic moving average of time series prediction that may be used in modeling and excel

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One 、 What is the linear moving average method ？

The second moving average method is to carry out the second moving average for the average value of the time series , Based on the last data of the time series composed of the first moving average and the second moving average, a linear model is established for prediction .

1 . The main features

• Moving average has the effect of smoothing or smoothing the original sequence , The fluctuation of the original sequence is weakened , And the average number of time interval terms N The bigger it is , The stronger the smoothing effect on the sequence .

• The number of moving average items should not be too large .

2. Insufficient

• Increase the number of periods of the moving average method （ Namely increase n value ） Will make the smooth fluctuation effect better , But it will make the predicted value less sensitive to the actual changes of the data ;
• The moving average method consists of a large number of records of past data ;

3. Calculation formula

$$S_t^1=\frac{Y_t+Y_y{-}_1+....+Y_t{-}_n{+}_1}{n}$$
$$S_t^2=\frac{S_t^1+S_t{-}_1^1+.....S_t{-}_n{+}_1^1}{n}$$
$$F_t{+}_T=a_t+b_{t}T$$
$$a_t=2S_t^1-S_t^2$$
$$b_t=\frac{2}{n-1}(S_t^1-S_t^2)$$
among ：
$$S_t^1$$ Is the value of the first average shift
$$S_t^2$$ Is the value of the second average shift

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Two 、 Operation steps

1. Prepare the data

We introduced the year - Water supply data , Pictured 2.1 Shown ,

2. Perform the first moving average

The specific operation is shown in the figure 2.2 Shown .PS: Note the position of the output area .

The result is as shown in the figure 2.3 Shown

3. Carry out the second moving average on the basis of the first moving average

Pictured 2.4 Operation shown , The interval is still selected 3,

The result is as shown in the figure 2.5 Shown

4. Put it into the formula to predict

We have the formula before ：
$$F_t{+}_T=a_t+b_{t}T$$
$$a_t=2S_t^1-S_t^2$$
$$b_t=\frac{2}{n-1}(S_t^1-S_t^2)$$
Suppose we want to predict 2022 Annual water supply , Then you can substitute the data into the formula
$$a_t=2\ast 19274.33-18669.67$$
$$b_t=\frac{2}{3-1}(19274.33-18669.67)$$
$$F_{(}2000+20)=2\ast 19274.33-18669.67+\frac{2}{3-1}(19274.33-18669.67)$$
Get F=20483.65

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3、 ... and summary

That's what we're going to talk about today , This paper simply introduces the application of the quadratic moving average method in Excel Simple operation of , and Excel Provides a large number of functions and methods that enable us to process data quickly and conveniently .