function z = bigshow (varargin)



%  function z = bigshow (a,b)

%  function z = bigshow (a,b,tsim,timpulse)

% This function takes a ARMA process of the form:

%

% a*y_t = b*w_t 

%

%  and graphs a simulation, the impulse response,

%  and the spectrum.

%  e.g., for

%  y_t = .9 y_{t-1} + w_t 

%  the input vectors would be:

%

%  a=[1 -.9]; and b=1;

%

%  The function would then be called:

%  

%  >> bigshow (a,b)



%a=[1 -.99]; b=1;  %  near random walk

%a=[1 0 0 0 -.8]; b=1;  %

%a=[1 -.8]; b=[1 -.7];  % muth process

%a=[1 -1.3 +.7]; b=1;    %  business cycle process



% Set up the input variables.



if nargin < 2 | nargin >4

   error ('Error.  Wrong number of input arguments.')

else

   if nargin == 4

      timpulse = varargin{4};

   else

      timpulse = 26;

   end;

   if nargin >= 3;

      tsim = varargin{3};

   else

      tsim = 70;

   end

   a = varargin{1};

   b = varargin{2};

end;



% first generate the simulation (Gaussian errors)

nn=100;   % number of observations to be discarded

u=randn(tsim+nn,1);

y=filter(b,a,u);

subplot(2,2,1),

axis ([0 tsim -Inf Inf]);

plot(y(nn+1:length(y)));

title ('Simulation');



%  Now generate the impulse response



subplot(2,2,2);

nn=timpulse;

y2=dimpulse(b,a,nn);

xx=[0:nn-1];  % fix the x axis to start at zero

y2=y2(1:nn);

%axis ([0 timpulse -Inf Inf]);

plot(xx',y2)

axis ([0 timpulse -Inf Inf]);



title ('Impulse Response')



%  Now generate the spectrum



n=256;

subplot(2,2,3);

%axis ([0 pi -1 1]);

[spect2,f2]=shownew(b,a,n);

title ('Log Spectrum')