dtfm.m

动态时间序列分析工具包.包括有ARMA,harmonic model,kalman filter等方法

function [tfs,fit,fitse,par,parse,e,y0] = dtfm(y,u,nn,TVP,nvr,P0,x0,smooth,ALG,nivit)
% DTFM  Multi-variable Dynamic Transfer Function estimation using instrumental variables
%
% [tfs,fit,fitse,par,parse,e,y0]=dtfm(y,u,nn,TVP,nvr,P0,x0,sm,ALG,niv)
%                                     1 2 3   4   5  6  7  8   9  10
%
% y: Time series (*)
% u: Input (*)
% nn: Model structure [na,nb(1:nu),nd(1:nu)] ([1 1 0])
% TVP: Model type for each TVP (0-RW, 1-IRW) (0)
% nvr: NVR hyper-parameters (0)
% P0: Initial P matrix (1e5)
% x0: Initial state vector (0)
% sm: Smoothing on (1-default) or off (0-saves memory)
% ALG: Smoothing algorithm: P (0) or Q (1-default)
% niv: Number of IV iterations (3)
%
% tfs: Transfer function (simulation) output
% fit: Model fit
% fitse: Standard error of the fit
% par: Parameter estimates
% parse: Standard errors of parameters
% e: Normalised innovations; use e=e(~isnan(e)) to remove NaNs
% y0: Interpolated data
%
% Example: dtfm(y, [u1 u2], [1 1 1 2 3], 0, 0.001)
%   transfer function type model y(k) = a(k)*y(k-1) + b1(k)*u1(k-2) + b2(k)*u2(k-3)
%   with RW models for both parameters (NVR=0.001)
%
% See also DTFMOPT, FCAST, STAND, DARX, DTFM

% Copyright (c) 2006 by CRES, Lancaster University, United Kingdom
% Authors : Peter Young, Wlodek Tych, Diego Pedregal, James Taylor
% Additional author: Paul McKenna

% The time series vector y (column) and input matrix u are 
% specified by the user. Each column of u represents an input 
% signal. The function automatically handles missing values in y. 
% In fact, y may be appended with additional NaNs to forecast or 
% backcast beyond the original series, as long as appropriate 
% values for u are also specified. The remaining input arguments 
% are optional. The DTF model structure is defined by nn, which 
% takes the form [n m d] where, in transfer function terms, n and 
% m are the number of denominator and numerator parameters 
% respectively, while d is the number of samples time delay. A 
% first order model with unity time delay and one numerator 
% parameter [1, 1, 1] is utilised by default.
% 
% TVP is a vector specifying the model associated with each 
% DARX model parameter, listed in order of each denominator 
% parameter and then the numerator parameters for each input
% Choices include a RW model by default (0) 
% or a IRW model (1). nvr is a vector of NVR hyperparameters 
% for each regressor where, for example, zero (default) implies 
% time invariant parameters. The initial state vector and diagonal 
% of the P-matrix may be specified using x0 and P0, with default 
% values of 0 and 1e5 respectively. FIS may be turned off by 
% changing sm from its default unity to 0. In this case, the model 
% fit and estimated parameters are their filtered values. This 
% speeds up the algorithm and reduces memory usage in cases 
% when smoothing is not required. Finally, either the P (0) or 
% default Q (1) smoothing algorithms are selected using the ALG 
% input argument. In general, should convergence problems be 
% encountered, changing the algorithm may help.
% 
% If the lengths of TVP, nvr, alpha, P0 or x0 are less than the 
% total number of parameters, then they are automatically 
% expanded to the correct dimensions by using the final element of 
% the specified input vector. For example, if the DTF model has 3 
% parameters but TVP is defined as [1 0], then TVP is 
% automatically expanded to [1 0 0]. Similarly, a scalar P0 implies 
% an identity matrix scaled by this value.
% 
% The function returns the simulation response tfs (with the same 
% dimensions as y), regression fit and parameters par (one column 
% for each parameter), together with the associated standard errors 
% in the latter two cases, fitse and parse. Here, tfs is based on 
% feeding the input signal through the model (the output signal is 
% not used, except to establish the initial conditions), while fit 
% represents the 1-step ahead predictions and is equivalent to the 
% fit returned by dlr.
% 
% The function also returns each of the linear components of the 
% model comp, i.e. the components associated with each input and 
% output and their past values, the normalised innovations 
% sequence e and interpolated data y0, where the latter consist of 
% the original series with any missing data replaced by the model. 
% Note that fit is the sum of the columns in comp, while the 
% normalised innovations are padded with initial NaNs to ensure 
% that the vector is the same size as y. If statistical tests on the 
% innovations are required, remove these NaNs with the command 
% e = e(~isnan(e)).

if nargin==0
  disp(' ')
  disp(' DTFM  Multi-variable Dynamic Transfer Function Estimation using Instrumental Variables')
  disp(' ')
  disp(' [tfs,fit,fitse,par,parse,e,y0]=dtfm(y,u,nn,TVP,nvr,P0,x0,sm,ALG,niv)')
  disp(' ')
  return
end

if nargin<10, nivit=[]; end
if nargin<9, ALG=[]; end
if nargin<8, smooth=[]; end
if nargin<7, x0=[]; end
if nargin<6, P0=[]; end
if nargin<5, nvr=[]; end
if nargin<4, TVP=[]; end
if nargin<3, nn=[]; end
if nargin<2, u=[]; end
if nargin<1, y=[]; end

[tfs,fit,fitse,par,parse,e,y0]=dtfm0(y,u,nn,TVP,nvr,P0,x0,smooth,ALG,nivit);

% end of m-file