garch.rar_GARCH MATLAB_matlab 控制_灰色_灰色 garch_灰色GARCH

function [coefficients, errors, LLF, innovations, sigma, summary] = garchfit(spec , y , X) %GARCHFIT Univariate GARCH process parameter estimation. % Given an observed univariate return series, estimate the parameters of a % conditional mean specification of ARMAX form and conditional variance % specification of GARCH form. The estimation process infers the innovations % from the return series and fits the model specification to the return % series by maximum likelihood. % % [Coeff,Errors,LLF,Innovations,Sigma,Summary] = garchfit(Series) % % [Coeff,Errors,LLF,Innovations,Sigma,Summary] = garchfit(Spec, Series) % [Coeff,Errors,LLF,Innovations,Sigma,Summary] = garchfit(Spec, Series, X) % % garchfit(...) % % Optional Input: Spec, X % % The first calling syntax is strictly a convenience form, modeling a return % series as a constant plus GARCH(1,1) conditionally Gaussian innovations. % For any models beyond this default (yet common) model, a specification % structure, Spec, must be provided. % % The second and third calling syntaxes allow the specification of much more % elaborate models for the conditional mean and variance processes. % % The last calling syntax (with no output arguments) will perform identical % estimation procedures as the first three, but will print the iterative % optimization information to the MATLAB command window along with the final % parameter estimates and standard errors. It will also produce a tiered plot % of the original return series as well as the innovations (i.e., residuals) % inferred, and the corresponding conditional standard deviations. % % Inputs: % Series - Vector of observations of the underlying univariate return series % of interest. Series is the response variable representing the time series % fit to conditional mean and variance specifications. The last element of % Series holds the most recent observation. % % Optional Inputs: % Spec - Structure specification for the conditional mean and variance models, % and optimization parameters. Spec is a structure with fields created by % calling the function GARCHSET. Type "help garchset" for details. % % X - Time series regression matrix of explanatory variable(s). Typically, X % is a regression matrix of asset returns (e.g., the return series of an % equity index). Each column of X is an individual time series used as an % explanatory variable in the regression component of the conditional mean. % In each column of X, the first row contains the oldest observation and % the last row the most recent. If X is specified, the most recent number % of valid (non-NaN) observations in each column of X must equal or exceed % the most recent number of valid observations in Series. When the number % of valid observations in each column of X exceeds that of Series, only % the most recent observations of X are used. If empty or missing, the % conditional mean will have no regression component. % % Outputs: % Coeff - Structure containing the estimated coefficients. Coeff is of the % same form as the Spec input structure, which allows other GARCH Toolbox % functions (e.g., GARCHSET, GARCHGET, GARCHSIM, and GARCHPRED) to accept % either Spec or Coeff seamlessly. % % Errors - Structure containing the estimation errors (i.e., the standard % errors) of the coefficients. The fields of Errors are a subset of those % found in Coeff or Spec, and correspond to the coefficient fields only. % % LLF - Optimized log-likelihood objective function value associated with the % parameter estimates found in Coeff. Optimization is performed by the % FMINCON function of the MATLAB Optimization Toolbox. % % Innovations - Innovations vector inferred from the input Series. The size % of Innovations is the same as the size of Series. % % Sigma - Conditional standard deviation vector corresponding to Innovations. % The size of Sigma is the same as the size of Series. % % Summary - Structure of summary information about the optimization process, % including convergence information, iterations, objective function calls, % active constraints, and the covariance matrix of coefficient estimates. % % See also GARCHSET, GARCHSIM, GARCHPRED, GARCHLLFN, FMINCON. % Copyright 1999-2002 The MathWorks, Inc. % $Revision: 1.9 $ $Date: 2002/03/11 19:37:16 $ % % References: % Bollerslev, T. (1986), "Generalized Autoregressive Conditional % Heteroskedasticity", Journal of Econometrics, vol. 31, pp. 307-327. % Box, G.E.P., Jenkins, G.M., Reinsel, G.C., "Time Series Analysis: % Forecasting and Control", 3rd edition, Prentice Hall, 1994. % Engle, Robert (1982), "Autoregressive Conditional Heteroskedasticity % with Estimates of the Variance of United Kingdom Inflation", % Econometrica, vol. 50, pp. 987-1007. % Hamilton, J.D., "Time Series Analysis", Princeton University Press, 1994. % % % Check input arguments. The single input case must specify a % valid numeric vector of returns. For the multiple input case, % the first input must be a specification structure. % switch nargin case 1 if isnumeric(spec) y = spec; spec = garchset; % Allow a convenience/default model form. else error(' Observed return series ''Series'' must be specified.'); end case {2 , 3} if ~isstruct(spec) error(' ''Spec'' must be a structure.'); end otherwise error(' Too many inputs specified.'); end % % Scrub the observed return series vector y(t). % rowY = logical(0); if prod(size(y)) == length(y) % Check for a vector (single return series). rowY = size(y,1) == 1; % Flag a row vector for outputs. y = y(:); % Convert to a column vector. else error(' Observed return series ''Series'' must be a vector.'); end % % The following code segment assumes that missing observations are indicated % by the presence of NaN's. Any initial rows with NaN's are removed, and % processing proceeds with the remaining block of contiguous non-NaN rows. % Put another way, NaN's are allowed, but they MUST appear as a contiguous % sequence in the initial rows of the y(t) vector. % i1 = find(isnan(y)); i2 = find(isnan(diff([y ; zeros(1,size(y,2))]) .* y)); if (length(i1) ~= length(i2)) | any(i1 - i2) error(' Only initial observations in ''Series'' may be missing (NaN''s).') end if any(sum(isnan(y)) == size(y,1)) error(' A realization of ''Series'' is completely missing (all NaN''s).') end firstValidRow = max(sum(isnan(y))) + 1; y = y(firstValidRow:end , :); % % Scrub the regression matrix and ensure the observed return series vector y(t) % and the regression matrix X(t) have the same number of valid (i.e., non-NaN) % rows (i.e., impose time index compatibility). During estimation, the innovations % process e(t) must be inferred from the conditional mean specification, which % may include a regression component if desired. In contrast to simulation, % estimation of the innovations process e(t) is NOT independent of X. % if (nargin >= 3) & ~isempty(X) if prod(size(X)) == length(X) % Check for a vector. X = X(:); % Convert to a column vector. end % % Retain the last contiguous block of non-NaN (i.e, non-missing valued) observations only. % if any(isnan(X(:))) X = X((max(find(isnan(sum(X,2)))) + 1):end , :); end if size(X,1) < size(y,1) error(' Regression matrix ''X'' has insufficient number of observations.'); else X = X(size(X,1) - (size(y,1) - 1):end , :); % Retain only the most recent samples. end % % Ensure number of re