A practical case of SPSS establishing a time series multiplication season model

Time series analysis-------multiplicative seasonal model

experiment name	Multiplicative season model
experiment content	Multiplicative season model
experiment purpose	2. Skilled in establishing multiplication season model

Recommended reading

1. Use Python to complete the basics of time series analysis
2. A practical case of SPSS establishing a time series multiplication season model
3. A practical case of SPSS establishing a time series additive seasonal model
4. Practical case of building a time series ARIMA model in Python

• Multiplication season model structure

 

Multiplication season model establishment

Draw a timing diagram

 

 

The time series chart shows that the series has a long-term growth trend and a seasonal effect with an annual cycle.

Difference smoothing

        Do a 1st-order 12-step difference to the original sequence, hoping to extract the trend effect and seasonal effect of the original sequence. The sequence diagram after the difference is as follows: 

Easy to get model stable

White noise test

       

 

 

 P<α, so the null hypothesis is rejected, that is, the sequence after the difference is a non-white noise sequence

 In summary: the sequence after the difference is a stationary non-white noise sequence, and the sequence after the difference needs to be further fitted to the ARMA model

Timing diagram

 

The autocorrelation graph shows that the autocorrelation coefficient of the 12th order delay is greater than twice the standard deviation, which indicates that the series still contains a very significant seasonal effect after the difference. The autocorrelation coefficient of the first order delay is also greater than 2 times the standard deviation. Have short-term relevance.     

1. Short-term correlation features: autocorrelation graphs and partial autocorrelation graphs show autocorrelation coefficients within 12 steps, ARMA(1,1),ARMA(1,0),ARMA(0,1) extract the short-term autocorrelation information of the differential sequence
2. Seasonal autocorrelation feature: The autocorrelation coefficient of the seasonal autocorrelation feature is truncated, and the partial autocorrelation coefficient is tailed. Here, the ARMA(0,1)12 model with a period of 12 steps can be used to extract the seasonal autocorrelation information of the sequence after the difference.

Parameter estimation and model checking

Based on the previous difference information, we have to establish ARIMA(1,1,1)*(0,1,1)12, ARIMA(1,1,0)*(0,1,1)12, ARIMA(0,1 ,1)*(0,1,1)12 model

 

• ARIMA(1,1,1)*(0,1,1)12

 

          

 P<α, the significance of the parameter fails the test

• ARIMA(0,1,1)*(0,1,1)12

 

Significance test of the model:

 

Modeling:

• ARIMA(1,1,0)*(0,1,1)12

                                                                                                                      The significance test of the parameter passed

 

Significance test of the model

 

Modeling:

 

Model prediction

 

 

 

 

 

> It's over here, if it helps you, welcome to like and follow, your likes are very important to me