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HET

The HET command implements maximum likelihood estimation of models which require corrections for heteroskedastic errors.

In general, the format is:

HET depvar indeps (exogs) / options

The available options are:

OPTION DESCRIPTION
arch= Specifies the order q of the ARCH process.
archm= Specifies the functional form for the ARCH-in-Mean term. Set ARCHM=0 for the log of the variance function and set ARCHM=0.5 for the square root of the variance function. When this option is used the model estimation uses numerical derivatives. The estimation algorithm provides a Hessian approximation that is used to compute the covariance matrix estimate. This may give unreliable standard errors. Therefore, the NUMCOV option (as described for the NL command) should also be considered with the ARCHM= option.
beg= Specifies the BEGinning observation to be used in estimation. This option overrides the SAMPLE command and defaults to the sample range in effect.
coef= Saves the COEFficients in the variable specified. If there is an intercept it will be stored as the last coefficient.
conv= Specifies the CONVergence criterion for the coefficients. This value will be multiplied by each coefficient starting value to compute the convergence condition for each coefficient. The default is CONV=.00001.
cov= Saves the COVariance matrix of coefficients in the variable specified.
dump DUMPS large amounts of output mainly useful to SHAZAM Consultants
end= Specifies the ENDing observation to be used in estimation. This option overrides the SAMPLE command and defaults to the sample range in effect.
garch= Specifies the order p of the lagged conditional variances in the GARCH process. If the ARCH= option is not set then the process estimated is GARCH(p,1). In applied work the GARCH process that is often considered practical is the GARCH(1,1) process. This is obtained by specifying GARCH=1.
gmatrix= Specifies an NxK matrix to use to store the derivatives of the log-likelihood function at each observation. This option is not available with the NUMERIC option.
iter= Specifies the maximum number of ITERations. The default is 100.
lininv Used when the dependent variable is LINear, but the independent variables are in INVerse form. This type of model is known as the reciprocal model. This option only affects the calculation of the elasticities. NOTE: This option does not transform the data. The data must be transformed by the user with the appropriate GENR commands or the Data Editor. See the chapter ORDINARY LEAST SQUARES in the SHAZAM Reference Manual.
linlog Used when the dependent variable is LINear, but the independent variables are in LOG form. This option only affects the calculation of the elasticities. NOTE: This option does not transform the data. The data must be transformed by the user with the appropriate GENR commands or the Data Editor. See the chapter ORDINARY LEAST SQUARES in the SHAZAM Reference Manual.
list LISTs and plots the residuals and predicted values of the dependent variable and residual statistics. When LIST is specified RSTAT is automatically turned on.
loginv Used when the dependent variable is in LOG form, and the independent variables are in INVerse form.
loglin Used when the dependent variable is in LOG form, but the independent variables are LINear. This option only affects the calculation of the elasticities. NOTE: This option does not transform the data. The data must be transformed by the user with the appropriate GENR commands or the Data Editor. See the chapter ORDINARY LEAST SQUARES in the SHAZAM Reference Manual.
loglog Used when the dependent variable is in LOG form, and the independent variables are in LOG form. This option only affects the calculation of the elasticities. NOTE: This option does not transform the data. The data must be transformed by the user with the appropriate GENR commands or the Data Editor. See the chapter ORDINARY LEAST SQUARES in the SHAZAM Reference Manual.
mach= Specifies the order of the moving average process in models with ARCH errors.
max Prints Analysis of Variance Tables, Variance-covariance matrix, Correlation matrix, Residuals, Residual Statistics and Goodness of Fit Test for Normality. This option is equivalent to using the ANOVA, LIST, PCOV, PCOR and GF options. Users should be sure the MAX output is necessary, otherwise unnecessary calculations are required.
method= Specifies the nonlinear algorithm to use for estimation. The default is a Davidon-Fletcher-Powell algorithm. An alternative METHOD=BFGS, Broyden-Fletcher-Goldfarb-Shanno (BFGS), is described in Belsley [1980]. Another alternative is a slightly different D-F-P algorithm which can be obtained with METHOD=DFP. Simulated Annealing is specified via METHOD=SA, which is described in Goffe et al [1994]. The default is ideal for large or complex nonlinear functions. For nearly linear or small problems an alternative algorithm may improve results.
model= Specifies the form of heteroskedasticity. The available options are: ARCH - for ARCH models DEPVAR - Dependent Variable Heteroskedasticity MULT - Multiplicative Heteroskedasticity STDLIN - Standard Deviation is a linear function of exogenous variables. If the ARCH=, ARCHM=, GARCH= or MACH= options are requested then MODEL=ARCH is assumed. Otherwise, the default is MODEL=DEPVAR. VARLIN - Variance is a linear function of exogenous variables
noconstant There will be NO CONSTANT (intercept) in the estimated equation. This option is used when the intercept is to be suppressed in the regression or when the user is supplying the intercept. This option should be used with caution as some of the usual output may be invalid. In particular, the usual R^2 is not well defined and could be negative. However, when this option is used, the raw moment R^2 may be of interest. The ANALYSIS OF VARIANCE - FROM MEAN table will not be computed if this option is used.
numcov Uses numeric differences to compute the covariance matrix after estimation. If this option is NOT specified SHAZAM uses a method based on the Davidon-Fletcher-Powell algorithm which builds up the covariance matrix after many iterations. This method may not be accurate if the model only runs for a small number of iterations. The numeric method is more expensive and also may not necessarily be accurate. The differential to be used in numeric differences can be controlled with the STEPSIZE= option.
numeric Uses the NUMERIC difference method to compute derivatives in the algorithm. SHAZAM normally computes analytic derivatives which are more accurate. However, in some models with many equations and parameters, considerable savings in required memory will result if the NUMERIC option is used to compute numeric derivatives. In some cases the NUMERIC option may even be faster. For large models SHAZAM may automatically switch to numeric derivatives. If this happens then analytic derivatives can be forced with the NONUMERIC option (this will not be effective if functions other than LOG() and EXP() are used in the model).
opgcov Uses the outer-product of the Gradient method to compute the covariance matrix. It is not valid with the NUMERIC option.
pcor Prints the CORrelation matrix of the estimated coefficients. This should not be confused with a correlation matrix of variables which can be obtained with a STAT command.
pcov Prints the COVariance matrix of coefficients. This should not be confused with the covariance matrix of variables which can be obtained with the STAT command.
piter= Specifies the frequency with which ITERations will be Printed in the output. The default PITER=15 indicates that one out of every 15 iterations will be printed.
predict= Saves the PREDICTed values of the dependent variable in the variable specified.
presamp Sets the initial value for the presample data in all iterations. The algorithm sets the pre-sample values as an additional parameter and then obtains an estimated value that maximizes the value of the likelihood function. Use the PRESAMP option to ensure that an initial value is fixed for the pre-sample data in all iterations. If this option is specified then the pre-sample values are set to the average of the squared errors evaluated at the starting parameter values or the square of the value specified in the START= option.
resid= Saves the values of the RESIDuals from the regression in the variable specified.
rstat Prints Residual Summary STATistics. The output includes the Durbin-Watson statistic and related residual test statistics. It also includes the Runs Test. When the LIST option is specified RSTAT is automatically turned on.
start= Specifies a vector of starting values for the estimation. The values must be in the same order as on the SHAZAM output. In addition, for ARCH models, the final parameter may be the starting value for the standard deviation of the pre-sample innovations. If this option is not specified then the starting parameter values are chosen by default. The default starting estimate for ? are obtained from an OLS regression. For ARCH models the default starting values for the ? are obtained from a regression of the OLS squared residuals on a constant and q lags.
stderr= Saves the values of the STanDard ERRors of the coefficients in the variable specified.
stdresid= Saves the standardized residuals in the variable specified. The standardized residuals are computed from the estimated parameters.
stepsize= Specifies the stepsize to use with the NUMCOV and NUMERIC options to control the differential in numeric derivatives. The default is STEPSIZE=1E-4. The calculated covariance matrix may be very sensitive to this value.
tratio= Saves the values of the T-RATIOs in the variable specified.
wide Uses a wider page width for the display of results. For printing, the page set-up should be set to landscape orientation.

Temporary variables that are available are: $ERR, $K, $LLF, $N and $R2OP