Bootstrapping

 

Introduction  Previous page  Next page

 

Most parameters and test statistics that SVAR can calculate can also be evaluated using bootstrapping. The two basic approaches that SVAR currently supports are parametric and non-parametric bootstrapping. The former means that new innovations are first drawn from a multivariate standard normal distribution. These innovations are then transformed into bootstrapped residuals by using the estimated covariance matrix from the original estimated residuals. The latter approach means that SVAR draws bootstrapped residuals from the original estimated residuals without replacement where each observation vector (in time) has an equal probability of being drawn. For the non-parametric approach the block size can also be selected, i.e., the program makes it possible to perform block bootstraps. With a block size equal to 1 we treat the estimated residuals as iid, while a block size greater than 1 yields dependence over time. For example, with a block size of 4 SVAR will use the residuals i, i+1, i+2, i+3 when the integer i is drawn. New data series for both approaches are constructed by taking the initial values and the estimated parameters as given. In some cases, SVAR needs to estimate new parameter values, such as for Wald tests, to ensure that the parameters used are consistent with the null hypothesis. The selection of bootstrapping approach is handled directly from each bootstrap dialog.

 

To set defaults for the bootstraps (and simulations) refer to the options available on the Simulation tab on the Preferences dialog. For example, there you can influence how the random number generator operates and how many replications to use by default.

 

To make use of bootstrapping you'll need to select the desired bootstrap dialog from the Simulation or Bootstrap menus (see, e.g., the Cointegration Rank Tests dialog). These menus are located on the Cointegration Rank Tests, Restrictions on (alpha,beta), and Identification & Estimation dialogs. Some statistics can be bootstrapped from all of these dialogs, others from only 1 or 2. This is directly related to the decision process when specifying a model. For example, the trace tests can only be bootstrapped from the Cointegration Rank Tests dialog.

 

It's also possible to perform bootstraps under fixed alternatives and to evaluate bootstraps using Monte Carlo. Such features have currently been implemented for the Nyblom Tests, and are planned to be implemented also for the other parameter constancy tests.