A Consistent Test of Stationary Ergodicity

TLDR: In this paper, a statistical test of stationary-ergodicity for known Markovian processes on R^d is presented. But it is not applicable to testing models and algorithms, as well as estimated time series processes ignoring the estimation error, since the test can be easily performed using any of a number of standard statistical and mathematical computer packages.

Abstract: A formal statistical test of stationary-ergodicity is developed for known Markovian processes on R^d. This makes it applicable to testing models and algorithms, as well as estimated time series processes ignoring the estimation error. The analysis is conducted by examining the asymptotic properties of the Markov operator on density space generated by the transition in the state space. The test is developed under the null of stationary-ergodicity, and it is shown to be consistent against the alternative of nonstationary-ergodicity. The test can be easily performed using any of a number of standard statistical and mathematical computer packages.

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Table I Monte Carlo Investigations of Size and Power Null of Stationary-Ergodicity 1000 simulations

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
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
   
  
    
 
 
 
  
   
 
  

    


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           
 
   
          
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



    

 

        
 

  





   



   
    

    

           
   
  
 
  
        
 
     
    
       
 

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 
 
 
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



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   
    

      

    
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 

 




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J

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

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J

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 
      






   

  



 

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
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
 
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






  

 
       

 
 
   
 

 

   

  


     
   


 
 
   

 
 


 
   

          

  
   



           
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Frequently asked questions

Q1. What are the contributions in "Division of the humanities and social sciences" ?

Domowitz and El-Gama this paper developed a statistical test of stationary ergodicity for known Markovian processes on a density space.