Statistics

 

A quick and dirty way of taking the number of degrees of freedom into account when performing inference. Typically, the original test is adjusted by multiplying by the number of degrees of freedom and dividing by the product between the number of observation and the number of restrictions. May in some cases have better small-sample properties.

 

If you don't have any exogenous variables in the model SVAR will also "Bartlett correct" the lag order (Wald and LM) tests when this option is checked. For these tests the correction formula is based on Corollary 5 in Omtzigt (2003), but since the tests are not LR tests the formula is not directly applicable. Moreover, the formula in Omtzigt is based on a model without deterministic variables. Hence, at best they provide approximate Bartlett correction factors.

 

If you have checked the "Serial Correlation Tests" box in the main program window, then this option enables the computation of the Ljung-Box test and writes the result to the output file.

 

When you have selected this option the Ljung-Box statistic is divided by the correction factor 1+[nr/2*(T-nr)], where T is the number of observations and nr is the number of regressors. For large T the correction factor is close to unity.

 

If you have checked the "Normality Tests" box in the main program window, then this option enables the computation of the "E_n" omnibus statistic (see Doornik and Hansen (1994)).

 

Writes results on 4 common (FPE, Akaike, Schwarz, and Hannan-Quinn) information criteria and the Fractional Marginal Likelihood (FML) to the output file. The FML criterion is asymptotically equal to the Schwarz Bayesian Information Criterion. For details on the FML model selection criterion, see Villani (2001b) for lag order and Corrander and Villani (2004) for cointegration rank comparisons.

 

Writes residual statistics (mean, standard deviation, skewness, kurtosis, min, max, R2, and residual correlations) to the output file.

 

When this option is check marked and the model includes additional deterministic variables, i.e., deterministic variables other than a constant, a linear trend and centered seasonal dummies, SVAR computes a number of tests on the parameters of these variables and writes the results to the output file. Currently, the tests include exclusion restrictions and long-run restrictions, where the latter are identical to the former when the number of cointegration vectors is either 0 and equal to the number of endogenous variables. In this case, the long-run restrictions are not computed.

 

By default, SVAR computes a multivariate ARCH test by constructing a sequence of unique squared residuals and regressing this series on a constant and its own first lag. Given n residuals, the number of unique squared residuals is n(n+1)/2, i.e., equal to the number of unique elements of the covariance matrix of the residuals. Based on the auxiliary regression results and the null hypothesis where all lagged values are zero, an LM test is calculated from the multivariate R-squared statistic using the restricted and unrestricted covariance matrix. If you check mark the current option, the regression coefficients are restricted such that only the diagonal elements of the lag matrix and the constant vector can be nonzero under the alternative hypothesis. This saves quite a few degrees of freedom, keeps the most interesting parameters under the alternative, but takes a little longer to calculate since a second step is added to the auxiliary regression.

 

This option influences the maximum lag order used when running the "Model Selection" function from the Tools menu on the main program window. The default value for this parameter is 12. If the model contains too many parameters relative to the size of the sample, SVAR will automatically lower the value for this parameter when applied in the Model Selection function. Moreover, if the maximum number of lags for the Lag Order control (see the Estimation page) is smaller than the maximum lag order for Model Selection, the lowest value of these two will be considered for the Model Selection function.

 

This parameter affects the variance of the noise, which is Gaussian with zero mean. It is possible to set the noise parameter to zero and thus remove the noise completely. Values between 0 and 1 are treated as valid, although small values are recommended. The default value is 0.01. Noise may be added to Wald tests which may have a singular asymptotic covariance matrix under the null hypothesis. Currently, the parameter is only used for the multi-step Granger causality tests; see Lütkepohl and Burda (1997) for details on the multi-step Granger causality test, where our noise parameter corresponds to λ in their notation.

 

If you'd like SVAR to test the selected lag order against alternatives, this option allows you to specify the upper and lower lag orders relative to your selected lag order. For example, suppose you pick a maximum lag order test horizon of "+/-2 lags" and your model has 2 lags. In that case, SVAR will perform lag order test for 2 lags against 3 and 4, respectively, and for 1 lag against 2. It will not test the null of 0 lags versus 2. On the other hand, if your model has 3 lags, then with the same value for the maximum lag order test horizon, SVAR will test the null of 3 lags versus 4 and 5 respectively, and of 1 lag and 2 lags against 3 lags, respectively.