# Moment calibration and correlations

Dear experts,

Based on the examples in the reference manual, I conclude that

moment_calibration;
y_obs,y_obs, [0.5, 1.5]; //[unconditional variance]
end;


imposes the variance of y_obs to be between 0.5 and 1.5. But is moment_calibration always about covariances? For example, is

moment_calibration;
y_obs,y_obs(-1), [0.4, 0.8];
end;


a bound on the autocovariance of y_obs rather than, say, the autocorrelation of y_obs?

If so, is there a straight forward way to impose bounds on correlations? I understand that one can exploit \rho_{xy} = \sigma_{xy} / (\sigma_{x} \times \sigma_{y}), where \rho_{xy} is the correlation between x and y, and \sigma_{xy} is the covariance. But I would like to impose bounds on \rho_{xy} directly, without having to restrict e.g. \sigma_{x} or \sigma_{y}.

D

From what I can see in matlab/endogenous_prior_restrictions.m · master · Dynare / dynare · GitLab around line 143, all restrictions are based on correlations, not covariances. The only exception is contemporaneous relations like

moment_calibration;
y_obs,y_obs, [0.4, 0.8];
end;


where it is the variance (the correlation would always be 1).
@rattoma should be able to clarify.

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