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armaspec

PURPOSE ^

Computes the spectral density for an AR- or ARMA-model.

SYNOPSIS ^

[R]=armaspec(C,A,s2,n)

DESCRIPTION ^

  ARMASPEC   Computes the spectral density for an AR- or ARMA-model. 
    The process is governed by the system equation 
      A(q) * x(t) = C(q) * sqrt(s2) * e(t)  
  
  S = armaspec(C,A,s2,n) 
  
  
  S   = Spectral density. [f1 S1; f2 S2; ... fn Sn] 
        (Frequencies in row 1 and spectral density in row 2.) 
  
  C   = Coefficients in C-polynomials. [1 c_1 ... c_nc] 
  A   = Coefficients in A-polynomials. [1 a_1 ... a_na] 
  s2  = Innovation variance. 
  n   = Number of calculated values. 
  
  Example: AR(2)-process. 
    S = armaspec(1,[1 1 0.9],1,500); 
    plot(S(:,1),S(:,2)) 
  Example: ARMA(4,2)-process. 
    S = armaspec([1 0.05 -0.88],[1 -2.06 1.64 -0.98 0.41],4.84e-6,500); 
    plot(S(:,1),S(:,2))

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [R]=armaspec(C,A,s2,n) 
002  
003 % ARMASPEC   Computes the spectral density for an AR- or ARMA-model. 
004 %   The process is governed by the system equation 
005 %     A(q) * x(t) = C(q) * sqrt(s2) * e(t)  
006 % 
007 % S = armaspec(C,A,s2,n) 
008 % 
009 % 
010 % S   = Spectral density. [f1 S1; f2 S2; ... fn Sn] 
011 %       (Frequencies in row 1 and spectral density in row 2.) 
012 % 
013 % C   = Coefficients in C-polynomials. [1 c_1 ... c_nc] 
014 % A   = Coefficients in A-polynomials. [1 a_1 ... a_na] 
015 % s2  = Innovation variance. 
016 % n   = Number of calculated values. 
017 % 
018 % Example: AR(2)-process. 
019 %   S = armaspec(1,[1 1 0.9],1,500); 
020 %   plot(S(:,1),S(:,2)) 
021 % Example: ARMA(4,2)-process. 
022 %   S = armaspec([1 0.05 -0.88],[1 -2.06 1.64 -0.98 0.41],4.84e-6,500); 
023 %   plot(S(:,1),S(:,2)) 
024  
025 % Copyright (c) 1997 by Pär Johannesson 
026 % Toolbox: Rainflow Cycles for Switching Processes V.1.0, 2-Oct-1997 
027  
028 [H,w]=freqz(C,A,n); 
029 R=real(s2*H.*conj(H)); 
030 f=w/(2*pi); 
031  
032 R = [f R]; 
033

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

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