ordinary least squares with ARMA errors
res=olsarma1(AR,MA,y,x,initown,namexos,bhat)
* 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 with 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
* namey = a time series, a real (nx1) vector or a string equal to the name of a time series or a (nx1) real vector between quotes
* arg1,...,argn = arguments which can be:
- a time series
- a real (nxp) vector
- a string equal to the name of a time series or a (nxp) real vector between quotes
- the string 'noprint' if the user doesn't want to print the results of the regression
- 'dropna' if the user wants to remove the NA values from the data
- 'init=own' if the user wants the function to impose starting values for the parameters
- 'beta=xxx' to fix the starting values of the coefficients of the regression if the user has given the option 'init=own'
- 'optfunc=optim' if the user wants to use the optim optimisation function (default: optimg)
- 'opt_nelmead=crit,nitermax' with crit the value of the convergence criterion in the Nelder-Meade optimisation function and nitermax the maximum number of iterations (default = 'opt_nelmead=2*%eps,1000')
- 'opt_optim=opts' where opts are options for optim that can be entered after the starting value of the parameters (default = 'opt_optim=,''ar'',1e6,1e6'')
- 'opt_convg=val' where val is the threshold on gradient norm (default = 'opt_convg=1e-5')
* 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
- res('prests') = boolean indicating the presence or absence of a time series in the regression
- res('namey') = name of the y variable
- res('namex') = name of the x variables
- res('dropna') = boolean indicating if NAs have been dropped
- res('bounds') = if there is a timeseries in the regression, the bounds of the regression
- res('nonna') = vector indicating position of non-NAs