ordinary least squares with ARMA errors
res=olsarma1(AR,MA,y,x,initown,namexos,bhat,optfunc,opt_optim)
* AR = a (nar x 1) or (1 x nar) string or real vector of parameters corresponding to the AR part of the error process
- if AR is a real then all parameters are estimated
- if AR is a string then all parameters in AR with an equality (such as '=0.5') are constrained to the given value (0.5 in the example)
- if AR is a string then it can contain inequality constraints; for instance '<0.5' indicates that coeff must be lower than 0.5
- if initown is set to %F, then the user can give any value to AR; only it size matters for the estimation process
- if initown is set to %F,
* MA = a (nmaf x 1) or (1 x nmaf) string or real vector of corresponding to the AR part of the error, with the same working as for AR
* y = dependent variable vector (nobs x 1)
* x = independent variables matrix (nobs x nvar)
* initown = a boolean indicating whether the program must use the entered values for AR, MA as starting values (%t if this is the case)
* namexos = a boolean indicating whether the program must use the entered values for AR, MA as starting values (%t if this is the case)
* bhat = the starting values of teh relation between y and x (if initown is set to %t; in the other case, it can be omitted; if given, it will be ignored)
optfunc = 'optimg' if the user wants to use the optim optimisation function (default: optim)
opt_optim = a tlist, collecting the options to the optimisation function
* res = a results tlist with
- res('meth') = 'ols with arma errors'
- res('y') = y data vector
- res('x') = x data matrix
- res('nobs') = # observations
- res('nvar') = # variables
- res('beta') = bhat
- res('yhat') = yhat
- res('resid') = residuals
- res('vcovar') = estimated variance-covariance matrix of beta
- res('sige') = estimated variance of the residuals
- res('sigu') = sum of squared residuals
- res('ser') = standard error of the regression
- res('tstat') = t-stats
- res('pvalue') = pvalue of the betas
- res('dw') = Durbin-Watson Statistic
- res('condindex') = multicolinearity cond index
- res('prescte') = boolean indicating the presence or absence of a constant in the regression
- res('llike') = the log-likelihood
- res('AR') = the estimated AR part of the residuals
- res('MA') = the estimated MA part of the residuals
- res('tAR') = the t-statistics of the AR part of the residuals
- res('tMA') = the t-statistics of the MA part of the residuals
- res('pvalues AR') = the p-values of the AR part of the residuals
- res('pvalues MA') = the p-values of the MA part of the residuals
- res('V') = the estimated variance of the innovations of the residuals
- res('AIC') = the value of the Akaïke Critrium
- res('BIC') = the value of the Schwarz Critrium
- res('grad') = the gradient at solution
- res('type') = the e4 type of the model