[Gretl-users] Bootstrap news

[Talha Yalta]

Thanks very much!!! Just in time before I need to do some
bootstrapping as a part of testing my results in my dissertation. It
works with the heteroscedasticity corrected OLS also right?
Cheers,
Talha


On 3/28/07, Allin Cottrell <cottrell at wfu.edu> wrote:
> Andreas K suggested a short while ago that gretl should offer
> various bootstrap options via the graphical interface (GUI).  I
> agreed at the time that this was a good idea.  Here's a note on
> progress so far (in CVS, and the current gretl snapshot for
> Windows).
>
> First, the limitation: all of the following new stuff applies only
> to single-equation models estimated via OLS.  (Though please note
> that we already offer bootstrapped confidence intervals for
> impulse response functions in relation to VARs.)
>
> When you estimate a model via OLS in the GUI, the model viewer
> window has a menu bar, including items labeled "Analysis" and
> "Tests".
>
> New under "Analysis": there's a "Bootstrap..." item.  This opens a
> dialog box where you get to make five choices:
>
> (1) The variable/coefficient to examine.
>
> (2) "Confidence interval" vs "Studentized confidence interval" vs
>      "P-value".
>
> (3) "Resampled residuals" vs "Simulate normal errors".
>
> (4) Number of replications (default 1000).
>
> (5) Show graph of bootstrap sampling distribution (no/yes).
>
> Notes:
>
> In relation to (1): you only get to examine one coefficient at a
> time by this particular means.
>
> On (2): the default (95%) confidence interval is based directly on
> the quantiles of the bootstrap coefficient estimates.  The
> "studentized" version is as per Davidson and MacKinnon's
> "Econometric Theory and Methods" (ETM), chapter 5: at each
> bootstrap replication a t-ratio is formed as (a) the difference
> between the current and the baseline coefficient estimate, divided
> by (b) the baseline estimated standard error.  Then the confidence
> interval is formed based on the quantiles of this t-ratio, as
> explained in ETM.  The "P-value" variant is, again, as explained
> in ETM.
>
> On (3): you get to choose between resampling with replacement of
> the original residuals (rescaled as suggested in ETM), and
> simulated normal errors with the empirically given variance.
> Andreas suggested including the option of "case resampling" (that
> is, resampling the (y, X) pairs rather than the residuals.  I have
> not implemented this to date for two reasons: first, it seems
> statistically dodgy, and second it is considerably more burdensome
> from the computational viewpoint. (You can economize substantially
> if the X matrix is treated as constant across the bootstrap
> replications.)
>
> Point (4) should be mostly self-explanatory.  However, when you're
> doing a (1 - alpha) confidence interval, then, as explained in
> ETM, it is desirable that alpha(B + 1)/2 is an integer (where B is
> the number of replications).  So gretl adjusts the user-chosen B
> value to ensure this is the case.
>
> Point (5) again should be self-explanatory: you can get gretl to
> make a graph of the density of the bootstrapped coefficient or
> t-ratio. This option employs gretl's kernel density estimation
> facility.
>
> The above all pertains to the "Analysis/Bootstrap" menu item.  In
> addition you have options under "Tests/Linear restrictions".  The
> restrictions dialog now has a "Use bootstrap" check box.  If you
> check this, you get a bootstrapped F-test for whatever set of
> linear restictions you have entered.  The methodology is as
> described in ETM for bootstrapped P-values.
>
> Autoregressive models: If the set of regressors includes the first
> lag of the dependent variable this should be handled correctly:
> the bootstrap data sets are calculated recursively, taking into
> account the autoregression.  Please note that higher-order
> autoregressions are _not_ currently recognized and handled
> appropriately.
>
> In script mode: For single-equation models estimated via OLS, you
> can append the --boot flag to the "restrict" command to get
> bootstrapped tests.  You can also set the default number of
> bootstrap replications using the "set" command with "bootrep"
> parameter.  For example:
>
>   set bootrep 10000
>
> Testing and comments welcome!
>
> Allin.
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