📄 subject re arma matlab code.htm

📁 这是时间序列的matlab程序应用
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<H3>Subject: Re: ARMA matlab code</H3><PRE>From: <A href="mailto:brown.m.w@nort.bwi.wec.com">brown.m.w@nort.bwi.wec.com</A> (Mark W. Brown)
Reply-To: <A href="mailto:brown.m.w@nort.bwi.wec.com">brown.m.w@nort.bwi.wec.com</A>
Newsgroups: comp.soft-sys.matlab
Subject: Re: ARMA matlab code
Date: Wed, 18 Oct 1995 14:02:41 GMT
Organization: Westinghouse Electronic Systems
Message-ID: &lt;<A href="mailto:DGnDoH.M75@tron.bwi.wec.com">DGnDoH.M75@tron.bwi.wec.com</A>&gt;
References: &lt;<A href="mailto:beser.813606352@aplcomm.jhuapl.edu">beser.813606352@aplcomm.jhuapl.edu</A>&gt;

In article &lt;<A href="mailto:beser.813606352@aplcomm.jhuapl.edu">beser.813606352@aplcomm.jhuapl.edu</A>&gt;, <A href="mailto:beser@aplcomm.jhuapl.edu">beser@aplcomm.jhuapl.edu</A> (Nick Beser) says:
&gt;
&gt;I am trying to track down any time series analysis matlab code (in particular
&gt;code that implements the ARMA (Autoregressive Model). 
&gt;
&gt;Thanks,
&gt;
&gt;Nick Beser
&gt;Johns Hopkins University

Nick,
  Here's some MATLAB code which computes the AR coefficients
and then plots the resulting power spectral density.

Example Usage:  % Given input time series X.
                % Want 3rd order AR coeffients.
                % Plot 128 points in frequency domain.
                [s,b] = arcoeff(3,X);
                [p,w] = pspect(s,b,128);
                semilogy(w,p);

This was orignially written under MATLAB 3.X.  I haven't used
it since then, so I hope it still works.  Hope this helps. :-)

-Mark-

--------------------------------------------------------------
function [s,b] = arcoeff(n,x)

% function [s,b] = arcoeff(n,x) returns the nth order
% autoregressive coefficients (b) and sigma (s) given
% a data vector (x).

% Compute the autocorrelation coefficients and find
% the zeroth order lag position:

zero = length(x);
ryy = xcorr(x,'unbiased');

% Initialize the size of some matrices:

d = zeros(n,1);
b = zeros(n,n);
s = zeros(n,1);

% Compute the first order as a special case:

d(1) = ryy(zero+1);
b(1,1) = -d(1)/ryy(zero);
s(1) = ryy(zero)*(1-abs(b(1,1))^2);

% Use the full Levinsons algorithm for orders =&gt; 2:

for m=2:n
  d(m) = ryy(zero+m);
  for k=1:m-1
    d(m) = d(m) + b(m-1,k)*ryy(zero+m-k);
  end
  b(m,m) = -d(m)/s(m-1);
  for k=1:m-1
    b(m,k) = b(m-1,k) + b(m,m)*b(m-1,m-k)';
  end
  s(m) = s(m-1)*(1-abs(b(m,m))^2);
end

% Return the desired sigma and autoregressive coefficients:

s = s(n);
b = b(n,:);

--------------------------------------------------------------
function [p,w] = pspect(s,b,N)

% function p = pspect(s,b) computes the autoregressive
% power spectral density (p) given the nth order AR
% coefficients (b) and sigma (s) computed from ARCOEFF.
% N samples of the PSD at frequencies (w) are returned.

% Compute the equivalent transfer function H:

[H,w] = freqz(1,[1 b],N);

% Compute the power spectral density function:

p = s*(H.*conj(H));

--------------------------------------------------------------
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