UCSD_GARCH 工具箱

function varargout = garchfit(spec, y, X, e0, s0, y0) %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, EGARCH, or GJR 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,Sigmas,Summary] = garchfit(Series) % % [Coeff,Errors,LLF,Innovations,Sigmas,Summary] = garchfit(Spec, Series) % [Coeff,Errors,LLF,Innovations,Sigmas,Summary] = garchfit(Spec, Series, X, % PreInnovations, PreSigmas, PreSeries) % % garchfit(...) % % Optional Input: Spec, X, PreInnovations, PreSigmas, PreSeries % % 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 - Time series column 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 row 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 or GARCHFIT. 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. % % PreInnovations - Time series column vector of pre-sample innovations (i.e., % residuals) upon which the recursive mean and variance models are % conditioned. This vector may have any number of rows, provided sufficient % observations exist to initialize the mean and variance equations. Thus, if % M and Q are the number of lagged innovations required by the conditional % mean and variance equations, respectively, then the PreInnovations vector % must have at least max(M,Q) rows. If the number of rows exceeds max(M,Q), % then only the last (i.e., most recent) max(M,Q) rows are used as pre-sample % observations. % % PreSigmas - Time series column vector of positive pre-sample conditional % standard deviations upon which the recursive variance model is conditioned. % This vector may have any number of rows, provided sufficient observations % exist to initialize the conditional variance equation. Thus, if P and Q % are the number of lagged conditional standard deviations and lagged % innovations required by the conditional variance equation, respectively, % then the PreSigmas vector must have at least P rows for GARCH and GJR % models, and at least max(P,Q) rows for EGARCH models. If the number of % rows exceeds the requirement, then only the last (i.e., most recent) rows % are used as pre-sample observations. % % PreSeries - Time series column vector of pre-sample observations of the % return series of interest upon which the recursive mean model is % conditioned. This vector may have any number of rows, provided sufficient % observations exist to initialize the conditional mean equation. Thus, if % R is the number of lagged observations of the return series required by % the conditional mean equation, then the PreSeries vector must have at % least R rows. If the number of rows exceeds R, then only the last (i.e., % most recent) R rows are used as pre-sample observations. % % 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, GARCHPRED, GARCHINFER) to % accept either Spec or Coeff seamlessly. % % Errors - Structure containing the estimation errors (i.e., the standard % errors) of the coefficients. Errors is of the same form as the Spec and % Coeff structures. In the event an error occurs calculating the standard % errors, all fields associated with estimated coefficients are set to NaN. % % LLF - Optimized log-likelihood objective function value associated with the % parameter estimates found in Coeff. Optimization is performed by the % FMINCON function of the Optimization Toolbox. % % Innovations - Innovations (i.e., residuals) time series column vector % inferred from the input Series. The size of Innovations is the same as % the size of Series. In the event of an error, Innovations will be a % vector of NaN's. % % Sigmas - Conditional standard deviation time series column vector % corresponding to Innovations. The size of Sigmas is the same as the size % of Series. In the event of an error, Sigmas will be a vector of NaN's. % % 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. % % Notes: % (1) When specified, the PreInnovations, PreSigmas, and PreSeries time series % column vectors contain user-specified pre-sample observations used to % infer the outputs Innovations and Sigmas. When these vectors are specified % and necessary, they MUST be specified together. This is an all-or-nothing % approach. In other words, if a user chooses to provide pre-sample data, % then ALL necessary pre-sample data for ALL 3 vectors must be specified. % (2) Although PreInnovations, PreSigmas, and PreSeries are companion inputs, % there are circumstances in which one or more may be empty. For example, a % GARCH(0,Q) (i.e., an ARCH(Q)) model does not require lagged conditional % variances, and thus PreSigmas could be empty ([]). Similarly, PreSeries % is only necessary when the mean equation has an auto-regressive component. % (3) If the conditional mean and/or conditional variance equation is not % recursive in any way, then certain pre-sample information is unnecessary % to jump-start the model(s). However, specifying redundant pre-sample % information is NOT an error, and any pr