Time Series Prediction Using Mixtures of Experts

 
 

 
 
    

  

  



  

 
    




 
    




! "




 
 

# $  

     


  


  

  

 
   
   %" 
 "  # % $& 

   


 ' 
  "     
 
     (
 " " ( )
*
 +(   +  ,--. #  * (   +( *"" 
    (     !" ( (  
 "   (

  "  / 
  
" 
 + " "    

-        
 


     

*"      
/


 " (
)
*
 
(

 !"  
  
"/
  (  (
 
"  
0(    "  1  
"   (      " --  "       , 
(
*) 
   

 / .

  "*
"   
  
 " --  


 


 
(
*) 
 "
(   +  
"

" (       "
(   "
(
 
"    

    
" *) * (( 
*          (
 +
/ 
 ( 
     
   
"  
 (   
   ,2-.   ' *"  + " 
 (    "
0( 
 

 " *
  (
 
  
 
 *  
  *) *"" 

/
 
  "    !"
    *" 
(
 )  
 2       
 
" 
 
  "  " * "  )  
 !"   * 3 (  
" 
 +     
  
 
+

  " " (( *  
4$5

 *    " +(  + 

  ,--. 6
  "   "  
 
(  
 
  " 

 



 2 
   "      " --  
" 
 + 

/
   
 *  (   7 

  485 
 
0(


   
(
*)   " 

  !" (  "     +
 "  ( *)  
 " -
" 
 +    
  "     
     ' "  
 " " --   (
  + 
 " (  (


    
   *     
 "   (

 
"

 "  
0(   
"  
 

  "*
" " --  
         +
   "  

/
  

 !
9


 ," " (   .

  4&5 
   
 
 :  9 4;5   

   , -.

    
  " " --  0(
 ,
 
 " *     .  "    * 
(
*)

     !" -- 4$5  
" (    
   !" +   
  

 
   "  
 
2,
.  

*) *"" 
 "


(  
  
 
      




*  *"

" +      ,
 (

.  
 
(  



4




     

  

,  


5  
(( 

$

 

*"  , 

  )
 (  
  (   2 (  










2 
 
 "  


  .  " +    




*" * * * (

 
 
   
 *  



 
 (  )


 " 9

 

 


 "     " + 
*)  
   ,  =  .  > $  "  " 

*)   
  
 ? = ,
   .   
 "           
 "   *  +  "

 



 (
 "  

, 


< ?. =



 "  *" " 

 "

, 

 ,




 



     " 

 
  




 

 
 " (  L  
  
/

' ($$ 
 *  :
> " "   +(   +    (
  + * "     (

  3
  "    -   :
> "  "   
 
  " + 
 "      " +
  "
(   +  (  
" " ( , . !"   >
"
  "  (      "   + 
    +   "     !" (  (
   (  
 3



  


    
(  (
 
E



"  
 *

 ( 
  " "  (
 ,  " 
.  
E "  +  "   
"     -  , 485  ("  (
.   3 
     (
  3
 "  

 
     (
  (

+ #*   
( )  

 " "

 

  


 (  " 

*) %  "   "  (  

     
 "   (
 " 
   " --,   
 *"(   
 


.



!"( )
     



 Æ
 
   

 " , 4$5.   ( 
 "   

) ($
 2 
  -") 4 5   (  (
 
  * 
(
/ *)    (

 
"    * 
  "  
   "   

!" (
 * " 
 
:
> 
  +


485

 
 " *  " (   
(
*) 
 +/ (   +   0(
 !"  "   
  

"    +
 ( , 4 5     " (
. J 
 

 " 
   "



*"      

 
 
E


4$5 *    " (  ( 
 ("   
  "  
  *   " (   ( " (    "  
  *
(
*) -   "      :
> , 485. ( )  " --,


.    (   
 


!"  " 
 +    
/

   

 (

 !"( 
 
H ( " +(   +   
   
  "
 *
(
*) "(" * "
   "    !*


  
  
E
 
  
   " 

  ( 
" 
(  


!"   !
9 !2 ," "

(   .   4&5 
 "  
 - ,  

  . 
(   :  

!"     
  (    !2   


     (( , ("     4;5.  ' " "*
   
"  (     , 45. " " --    *    
E
 " - ,
 
 0(
  " !2  . !"  
 "   

     ( 
    " +(   +   ((  
  

  *  +  
 
   "   
 (
 
45

' "( 
 " * " 
(    
(  + 
 / 
 "  
  " -- *" "  "  '    "   
" 
"   *    /*  '"( 
3
/(

     * (
 "  
  " -- *" 
 +  (

      *" "  "  ,(" 


 



(
*).

   "
(   (   (
 
45

-   "   

    
( 
 
(  

 "  

   
" *) * " ((  
 

/
     




    !" +(  +    ,--. " 
 
     "  
*  *"  (
 "    
    *" "    " 


   ' " " "  (  " ( *  
"
 " --   
/ "  * (   " (   /     " 3    
 
 
  


  4>5 *E 
N

 
 '"  # M- 3  -  *"  

 K /

& 
  '
 

 $G  / 8 >8$

4$5 B
 - 
 B 2 M# " -+(   +  
 " "N

(    


 ;  >8>/$> >

45 - 6 
 -  6 M+
1(
  " A(

 


(, 2 .  % ( 
 -+( % *)N (   (
    


>;

45 -
 : 
 !*   2  ,>.

)  
 
      


 /6  

 4 5 -") # ,>;. M% ( % *)  K +
 " 
 
  A(

N 4;5 :  -1

(    


 8,>.  >;/>&&

(

 
 (
  
    "
  

:  % * O) >88 4&5 !
 #

  )  
(

    "



  6 /

 % * O) >8 485 7  B -  2 
 - 6 M 1(
  A(

 +/ 

 

 -+(   + N  :( />$  /  


  
 ! "

 >  45 7  B -  2 
   2B M%
/
 -   !   
 -+(   + N  :( />    


  
 ! "

 >;