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discar

PURPOSE ^

Discretizes an AR(1) process.

SYNOPSIS ^

[P,uu] = discar(u,a1,m,s)

DESCRIPTION ^

  DISCAR   Discretizes an AR(1) process. 
      System equation: X(k) = -a1*X(k-1) + e(k),  e(k) = N(m,s^2) 
  
  P = discar(u,a1,s,m) 
  
  P = Transition matrix, 
      P(i,j) = P ( u(j)<X(k)<u(j+1) |  u(i)<X(k-1)<u(i+1) ) 
  
  u  = Discretization levels. 
  a1 = System parameter. 
  m  = Innovation mean. 
  s  = Innovation std.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [P,uu] = discar(u,a1,m,s) 
002  
003 % DISCAR   Discretizes an AR(1) process. 
004 %     System equation: X(k) = -a1*X(k-1) + e(k),  e(k) = N(m,s^2) 
005 % 
006 % P = discar(u,a1,s,m) 
007 % 
008 % P = Transition matrix, 
009 %     P(i,j) = P ( u(j)<X(k)<u(j+1) |  u(i)<X(k-1)<u(i+1) ) 
010 % 
011 % u  = Discretization levels. 
012 % a1 = System parameter. 
013 % m  = Innovation mean. 
014 % s  = Innovation std. 
015  
016 % Copyright (c) 1997 by Pär Johannesson 
017 % Toolbox: Rainflow Cycles for Switching Processes V.1.0, 2-Oct-1997 
018  
019 n = length(u); 
020 PP = zeros(n-1,n-1); 
021 tol =2e-1; 
022  
023 for i = 1:n-1 
024   fprintf(1,'   i = %d\n',i); 
025  
026   % P(i,j) = P ( u(j)<X(k)<u(j+1) ,  u(i)<X(k-1)<u(i+1) ) 
027   for j = 1:n-1 
028     PP(i,j) = quad8('f_ar',u(i),u(i+1),tol,[],u(j),u(j+1),a1,m,s); 
029   end 
030  
031   % Pi = P ( u(i)<X(k)<u(i+1) ) 
032 %  Pi = normcdf((u(i+1)-m)*sqrt(1-a1^2)/s)-normcdf((u(i)-m)*sqrt(1-a1^2)/s); 
033  
034   % P(i,j) = P ( u(j)<X(k)<u(j+1) |  u(i)<X(k-1)<u(i+1) ) 
035 %  if Pi == 0  % Prob. outside working precision 
036 %    PP(i,:) = PP(i,:)/sum(PP(i,:)); 
037 %  else 
038 %    PP(i,:) = PP(i,:)/Pi; 
039 %  end 
040 end 
041  
042 P = PP; 
043 uu = (u(1:n-1)+u(2:n))/2; 
044

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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