line source
+ − function varargout = ltpda_arma_time(varargin)
+ − % LTPDA_ARMA_TIME estimates the ARMA parameters of the transfer function
+ − % relating an output to an input
+ − %
+ − %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ − %
+ − % DESCRIPTION: LTPDA_ARMA_TIME estimates the ARMA parameters of the
+ − % transfer function relating an output to an input time series. The
+ − % algorithm uses the IV method to find a set of initial parameters
+ − % and then performs an iterative search based on the Optimization
+ − % Toolbox.
+ − %
+ − % CALL: b = ltpda_arma_time(ax,ay,pl)
+ − %
+ − % INPUTS: ax - analysis object containig the input time series
+ − % ay - analysis object containig the output time series
+ − % pl - parameters list
+ − %
+ − % OUTPUTS: b - cdata type analysis object containing the ARMA
+ − % parameters and the residual of the fit
+ − %
+ − % PARAMETERS:
+ − % MaxIter - Maximum number of iterations to be performed by the
+ − % iterative search (default 4e2)
+ − % MaxFunEvals - Maximum number of function evaluations (default 1e2)
+ − % TolX - Tolerance on the estimated parameter (default 1e-6)
+ − % TolFun - Tolerance on the evaluated function (default 1e-6)
+ − % UpBound - Array of parameters upper bounds for the iterative search
+ − % (default is 1 for each parameter)
+ − % LowBound - Array of parameters lower bounds for the iterative search
+ − % (default is 1 for each parameter)
+ − % ARMANum - MA order of the ARMA filter (default 2)
+ − % ARMADen - AR order of the ARMA filter (default 1)
+ − %
+ − % VERSION: $Id: ltpda_arma_time.m,v 1.1 2008/03/04 12:55:05 miquel Exp $
+ − %
+ − % HISTORY: 15-02-2008 M Nofrarias
+ − % Creation
+ − %
+ − %
+ − % TODO: - Add parameters errors
+ − % - Pass from univariate to multivariate
+ − %
+ − %
+ − %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ −
+ −
+ −
+ − %% Standard history variables
+ −
+ − ALGONAME = mfilename;
+ − VERSION = '$Id: ltpda_arma_time.m,v 1.1 2008/03/04 12:55:05 miquel Exp $';
+ − CATEGORY = 'SIGPROC';
+ −
+ −
+ − %% Check if this is a call for parameters
+ − if nargin == 1 && ischar(varargin{1})
+ − in = char(varargin{1});
+ − if strcmpi(in, 'Params')
+ − varargout{1} = getDefaultPL();
+ − return
+ − elseif strcmpi(in, 'Version')
+ − varargout{1} = VERSION;
+ − return
+ − elseif strcmpi(in, 'Category')
+ − varargout{1} = CATEGORY;
+ − return
+ − end
+ − end
+ −
+ − %% Capture input variables names
+ − invars = {};
+ − as = [];
+ − ps = [];
+ − for j=1:nargin
+ − invars = [invars cellstr(inputname(j))];
+ − if isa(varargin{j}, 'ao')
+ − as = [as varargin{j}];
+ − end
+ − if isa(varargin{j}, 'plist')
+ − ps = [ps varargin{j}];
+ − end
+ − end
+ −
+ −
+ − %% Check plist
+ − if isempty(ps)
+ − pl = getDefaultPL();
+ − else
+ − pl = combine(ps, getDefaultPL);
+ − end
+ −
+ −
+ − %% Initialise variables
+ − x=as(1).data.y;
+ − y=as(2).data.y;
+ − p = find(pl, 'ARMANum');
+ − q = find(pl, 'ARMADen');
+ − disp(sprintf('! ARMA orders p = %d, q = %d', p,q))
+ −
+ − %% First estimate through Instrument Variables (IV) Method
+ −
+ − % Least squares
+ − for i=1:p
+ − obs1(:,i) = [zeros(i,1); x(1:length(x)-i)];
+ − end
+ − for i=1:q
+ − obs2(:,i) = [zeros(i,1); -y(1:length(y)-i)];
+ − end
+ −
+ − % LS estimation
+ − obs = [obs1 obs2];
+ − par0=(obs'*obs)\obs'*y
+ −
+ − % filter observations with LS parameters
+ − obs1_f = filter([par0(1:p)],[1 par0(p+1:p+q)],obs1);
+ −
+ − % build instruments
+ − inst = [obs1 obs1_f];
+ −
+ − % IV estimation
+ − par0=(inst'*obs)\inst'*y
+ −
+ −
+ − %% Iterative search using the Optimization Toolbox
+ −
+ −
+ − % Options for the lsqcurvefit function
+ − opt = optimset(...
+ − 'MaxIter',find(pl, 'MaxIter'),...
+ − 'TolX',find(pl, 'TolXm'),...
+ − 'TolFun',find(pl, 'TolFun'),...
+ − 'MaxFunEvals',find(pl, 'MaxFunEvals'),...
+ − 'Display','off');
+ −
+ − % Upper and Lower Bounds for the parameters
+ − ub=find(pl,'UpBound');
+ − lb=find(pl,'LowBound');
+ − if isempty(ub)
+ − ub=ones(p+q,1);
+ − pl = append(pl, param('UpBound', ub));
+ − disp('! Parameters Upper Bound set to 1')
+ − end
+ − if isempty(lb)
+ − lb=-ones(p+q,1);
+ − pl = append(pl, param('LowBound', lb));
+ − disp('! Parameters Lower Bound set to -1')
+ − end
+ −
+ − % Call to the Optimization Toolbox function
+ − [par,res]=lsqcurvefit(@(par,xdata)filter([par(1:p)],[1 par(p+1:p+q)],xdata),...
+ − par0,x,y,lb,ub,opt);
+ −
+ −
+ − %% Build output ao
+ −
+ − % New output history
+ − h = history(ALGONAME, VERSION, pl,[as(1).hist as(2).hist]);
+ − h = set(h,'invars', invars);
+ −
+ − % Make output analysis object
+ − b = ao([par; res]);
+ −
+ − % Name, mfilename, description for this object
+ − b = setnh(b,...
+ − 'name', ['ARMA param. Input: ' sprintf('%s ', char(invars{1})) ' Output: ' char(invars{2})],...
+ − 'mfilename', ALGONAME, ...
+ − 'description', find(pl,'description'),...
+ − 'hist', h);
+ −
+ − varargout{1} = b;
+ −
+ −
+ − %% --- FUNCTIONS ---
+ −
+ −
+ − % Get default parameters
+ − function plo = getDefaultPL();
+ − disp('* creating default plist...');
+ − plo = plist();
+ − plo = append(plo, param('MaxIter',4e2));
+ − plo = append(plo, param('MaxFunEvals',1e2));
+ − plo = append(plo, param('TolX',1e-6));
+ − plo = append(plo, param('TolFun',1e-6));
+ − plo = append(plo, param('ARMANum',2));
+ − plo = append(plo, param('ARMADen',1));
+ − disp('* done.');