A commonly used statistical modeling method -- difference analysis

1、 effect

Difference , In essence, it is the next value minus the previous value , It is mainly to eliminate some fluctuations and make the data tend to be stable , Nonstationary sequences can be obtained by Differential transformation Into a stationary sequence .

2、 Input / output description

Input ：１ Time Quantitative variables of sequence data
Output ： After the specified order difference Sequence diagram

3、 Learning Websites

SPSSPRO- Free professional online data analysis platform

4、 Case example

Case study ： Based on a magazine 1995-2019 Annual printing volume data , The first-order difference and the second-order difference are carried out respectively .

5、 Case data

Differential analysis of case data

6、 Case operation

Step1： New analysis ;
Step2： Upload data ;
Step3： Select the corresponding data to open and preview , Click start analysis after confirmation ;

step4： choice 【 Differential analysis 】;
step5： View the corresponding data format ,【 Differential analysis 】 Request input １ Quantitative variables of time series data .
step6： Set the difference order （ Be careful ： Select the differential class , Generally speaking, more than the second-order difference has no reference significance in statistics ）
step7： Click on 【 To analyze 】, Complete the operation .

7、 Output result analysis

Output results 1： Original sequence diagram

Chart description ： The figure above shows the original figure without difference . among X The axis represents the time item （ year ）,Y The axis represents the value （ Magazine print volume ）. Subjectively , The original sequence diagram has an increasing trend , Is a nonstationary sequence . We need to convert the non-stationary original sequence diagram into a stationary sequence by difference .

Output results 2： First order difference graph

Chart description ： The figure above shows the result of the first-order difference . When the time intervals are equal , Use the next value , Subtract the previous value , Get the first-order difference . Subjectively , The first-order difference sequence is numerically 1.5 Up and down , There is no obvious increasing and decreasing trend , It is preliminarily judged that the first-order difference sequence is a stationary sequence . In order to avoid artificial subjective judgment , Can pass ADF The unit root test is used to judge whether the first-order difference sequence is stable .

Output results 3： Second order difference graph

Chart description ： The figure above shows the result of the second-order difference . Do the same action twice , That is, on the basis of the first-order difference, the latter value is subtracted by another value , Call “ Second order difference ”. For the stationary test of the second order difference sequence , Can pass ADF The unit root test is used to judge whether the second-order difference sequence is stable .

8、 matters needing attention

• In general, you can go through ADF Test to quantitatively evaluate the numerical difference , Whether there is stability

9、 Model theory

10、 reference

[1]  Yao Zhipeng , He Dan , Cui Wei ． Differential and integral calculus ： Central China Normal University Press ,2015.05