arima.zip_MATLAB arima_arima matlab_matlab_matlab arima_sarima

function varargout = estimate(Mdl, YData, varargin) %ESTIMATE Estimate ARIMA model parameters % % Syntax: % % [EstMdl,EstParamCov,logL,info] = estimate(Mdl,Y) % [EstMdl,EstParamCov,logL,info] = estimate(Mdl,Y,param1,val1,...) % % Description: % % Given an observed univariate time series, estimate the parameters of an % ARIMA model. The estimation process infers the residuals of the % underlying response series and then fits the model to the response data % via maximum likelihood. % % Input Arguments: % % Mdl - ARIMA model specification object, as produced by the ARIMA % constructor or ARIMA/ESTIMATE method. % % Y - Response data whose residuals and conditional variances are inferred % and to which the model Mdl is fit. Y is a column vector, and therefore % a single path of the underlying series. The last observation of Y is % the most recent. % % Optional Input Parameter Name/Value Pairs: % % 'Y0' Presample response data, providing initial values for the % model. Y0 is a column vector, and may have any number of % rows, provided at least Mdl.P observations exist to % initialize the model. If the number of rows exceeds Mdl.P, % then only the most recent Mdl.P observations are used. If % Y0 is unspecified, any necessary observations are backcasted % (i.e., backward forecasted). The last row contains the most % recent observation. % % 'E0' Mean-zero presample innovations, providing initial values % for the model. E0 is a column vector, and may have any % number of rows, provided sufficient observations exist to % initialize the ARIMA model as well as any conditional % variance model (the number of observations required is at % least Mdl.Q, but may be more if a conditional variance % model is included). If the number of rows exceeds the % number necessary, then only the most recent observations % are used. If E0 is unspecified, any necessary observations % are set to zero. The last row contains the most recent % observation. % % 'V0' Positive presample conditional variances, providing initial % values for any conditional variance model; if the variance % of the model is constant, then V0 is unnecessary. V0 is a % column vector, and may have any number of rows, provided % sufficient observations exist to initialize the variance % model. If the number of rows exceeds the number necessary, % then only the most recent observations are used. If V0 is % unspecified, any necessary observations are set to the % average squared value of the inferred residuals. The last % row contains the most recent observation. % % 'X' Matrix of predictor data used to include a regression % component in the conditional mean. Each column of X is a % separate time series, and the last row of each contains % the most recent observation of each series. When presample % responses Y0 are specified, the number of observations in % X must equal or exceed the number of observations in Y; in % the absence of presample responses, the number of observations % in X must equal or exceed the number of observations in Y % plus Mdl.P. When the number of observations in X exceeds % the number necessary, only the most recent observations % are used. If missing, the conditional mean will have no % regression component regardless of the presence of any % regression coefficients found in the model. % % 'Options' Optimization options created with OPTIMOPTIONS (or OPTIMSET). % If specified, default optimization parameters are replaced % by those in options. The default is an OPTIMOPTIONS object % designed for the optimization function FMINCON, with % 'Algorithm' = 'sqp' and 'TolCon' = 1e-7. See documentation % for OPTIMOPTIONS (or OPTIMSET) and FMINCON for details. % % 'Constant0' Scalar initial estimate of the constant of the model. If % missing, an initial estimate is derived from standard time % series techniques. % % 'AR0' Vector of initial estimates of non-seasonal autoregressive % coefficients. The number of coefficients in AR0 must equal % the number of non-zero coefficients associated with the AR % polynomial (excluding lag zero). If missing, initial % estimates are derived from standard time series techniques. % % 'SAR0' Vector of initial estimates of seasonal autoregressive % coefficients. The number of coefficients in SAR0 must equal % the number of non-zero coefficients associated with the % SAR polynomial (excluding lag zero). If missing, initial % estimates are derived from standard time series techniques. % % 'MA0' Vector of initial estimates of non-seasonal moving average % coefficients. The number of coefficients in MA0 must equal % the number of non-zero coefficients associated with the % MA polynomial (excluding lag zero). If missing, initial % estimates are derived from standard time series techniques. % % 'SMA0' Vector of initial estimates of seasonal moving average % coefficients. The number of coefficients in SMA0 must equal % the number of non-zero coefficients associated with the % SMA polynomial (excluding lag zero). If missing, initial % estimates are derived from standard time series techniques. % % 'Beta0' Vector of initial estimates of the regression coefficients. % The number of coefficients in Beta0 must equal the number % of columns in the predictor data matrix X (see above). If % missing, initial estimates are derived from standard time % series techniques. % % 'DoF0' Scalar initial estimate of the degrees-of-freedom parameter % (used for t distributions only, and must exceed 2). If % missing, the initial estimate is 10. % % 'Variance0' A positive scalar initial variance estimate associated with % a constant-variance model, or a cell vector of parameter % name-value pairs of initial estimates associated with a % conditional variance model. As a cell vector, the parameter % names must be valid coefficients recognized by the variance % model. If missing, initial estimates are derived from % standard time series techniques. % % 'Display' String or cell vector of strings indicating what information % to display in the command window. Values are: % % VALUE DISPLAY % % o 'off' No display to the command window. % % o 'params' Display maximum likelihood parameter % estimates, standard errors, and t statistics. % This is the default. % % o 'iter' Display iterative optimization information. % % o 'diagnostics' Display optimization diagnostics. % % o 'full' Display 'params', 'iter', and 'diagnostics'. % % Output Arguments: % % EstMdl - An updated ARIMA model specification object containing the % par