ar1signv.m

蒙托卡罗模拟奇异谱分析

  function [g,a,c,g0,a0,c0]=ar1signv(x,sig)
% AR1SIGNV - AR(1) model estimation for noise component of data.
% Syntax: [g,a,c,g0,a0,c0]=ar1signv(x,sig);
% Naively estimates the parameters for a composite null-hypothesis
% of signal + AR(1) noise. The signal is subtracted from the data,
% and the AR(1) parameters are estimated from the residual.  
%
% Input:  x - the data vector.
%       sig - the signal vector
%
% Output: g  - estimate of the lag-one noise autocorrelation.
%         a  - estimate of the noise innovation variance.
%         c  - estimated lag-zero covariance of the noise. 
%         g0 - poor estimate of the lag-one noise autocorrelation.
%         a0 - poor estimate of the noise innovation variance.
%         c0 - poorly estimated lag-zero covariance of the noise. 
%
% Written by Eric Breitenberger.      Version 1/21/96
% Please send comments and suggestions to [e-mail]       
%

x=x(:);
sig=sig(:);
N=length(x);
if length(sig)~=N, error('Data and signal must have same length.'), end

% Noise model:
n=x-sig;

% Lag zero and one covariance estimates:
c0=n'*n/N;
c1n=n(1:N-1)'*n(2:N)/(N-1);
c0x=x'*x/N;
c1x=x(1:N-1)'*x(2:N)/(N-1);
c0s=sig'*sig/N;
c1s=sig(1:N-1)'*sig(2:N)/(N-1);

% Really naive estimate based on noise variance:
g0=c1n/c0;
a0=sqrt((1-g0^2)*c0);

% A better method: Subtract model covar. from data covar.
c=c0x-c0s;
g=(c1x-c1s)/c;
a=sqrt((1-g^2)*c);