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olsarma1

ordinary least squares with ARMA errors

CALLING SEQUENCE

res=olsarma1(AR,MA,y,x,initown,namexos,bhat,optfunc,opt_optim)

PARAMETERS

Input

* 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

 

Output

* 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

DESCRIPTION

Performs the estimation of an ols model with arma errors, with entries constrained to be matrices.

EXAMPLE

1) res=olsarma1(grocer_AR,grocer_MA,y,x,grocer_initown,grocer_beta)
2) res=olsarma1(0.4,[0.5 0.1],y,x,%T,[0.2 ; 0.1 ;-0.3])
// Example 1 is taken from function oslarma. Example 2 estimates and ols model with 3 exogenous variables, ARMA(1,2) errors, starting values given by the user.

AUTHOR

Eric Dubois 2010

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